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Quasiperiodic birhythmicity in a multicycle van der Pol oscillator. (English) Zbl 07920641

Belhaq, Mohamed (ed.), Advances in nonlinear dynamics and control of mechanical and physical systems. Selected articles from CSNDD, Marrakesh, Morocco, May 15–17, 2023. Singapore: Springer. Springer Proc. Phys. 301, 23-37 (2024).

MSC: 34C15 34C25

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Sanchis, Roberto; Miguel-Escrig, Oscar; Romero-Pérez, Julio-Ariel

Experimental tuning of PI controllers with symmetric send-on-delta sampling from the step response. (English) Zbl 1533.93214

Int. J. Control 97, No. 1, 101-110 (2024).

MSC: 93B52 93C65

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Cheng, Mengyu; Hao, Zimo; Röckner, Michael

Strong and weak convergence for the averaging principle of DDSDE with singular drift. (English) Zbl 07824115

Bernoulli 30, No. 2, 1586-1610 (2024).

MSC: 60H10 60H15 34C29 35R60 60G22

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Boschi, Martina; Ritelli, Daniele; Spaletta, Giulia

Exact time-integral inversion via Čebyšëv quintic approximations for nonlinear oscillators. (English) Zbl 1540.34078

J. Math. Anal. Appl. 533, No. 1, Article ID 128015, 16 p. (2024).

MSC: 34C15 34A45 33C75 41A50

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Chaffey, Thomas; Banert, Sebastian; Giselsson, Pontus; Pates, Richard

Circuit analysis using monotone+skew splitting. (English) Zbl 1530.94075

Eur. J. Control 74, Article ID 100854, 7 p. (2023).

MSC: 94C60 47N70

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Cheng, Mengyu; Liu, Zhenxin; Röckner, Michael

Averaging principle for stochastic complex Ginzburg-Landau equations. (English) Zbl 1517.35218

J. Differ. Equations 368, 58-104 (2023).

MSC: 35Q56 60H15 37B20 35B41 82D55 82D50 35R06 35R60

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Cheng, Mengyu; Liu, Zhenxin

The second Bogolyubov theorem and global averaging principle for SPDEs with monotone coefficients. (English) Zbl 1518.70024

SIAM J. Math. Anal. 55, No. 2, 1100-1144 (2023).

MSC: 70K65 70K42 70K43 70L10 60H15

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Kogelbauer, Florian; Breunung, Thomas

When does the method of harmonic balance give a correct prediction for mechanical systems? (English) Zbl 1517.37089

Appl. Anal. 102, No. 2, 425-443 (2023).

MSC: 37M99 49M15 70K42

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Argatov, I.; Voll, L.; Popov, V. L.

A hysteretic model of localized frictional contacts with instrumental stiffness. (English) Zbl 1528.74082

Meccanica 57, No. 8, 1783-1799 (2022).

MSC: 74M15 74M10 74H45

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de Castilho, William; Salinas, S. R.

Spherical model with Dzyaloshinskii-Moriya interactions. (English) Zbl 1539.82061

J. Stat. Mech. Theory Exp. 2022, No. 7, Article ID 073106, 13 p. (2022).

MSC: 82B23 82B20 82B26

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Zhang, J. M.; Song, H. F.; Liu, Y.

Permanent variational wave functions for bosons. (English) Zbl 1494.82030

Physica A 599, Article ID 127399, 30 p. (2022).

MSC: 82D05 81V70

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Liu, Xin; Wang, Yan

Averaging principle on infinite intervals for stochastic ordinary differential equations with Lévy noise. (English) Zbl 1484.60063

AIMS Math. 6, No. 5, 5316-5350 (2021).

MSC: 60H10 34C27 34C29 37B20 60G51

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Miguel-Escrig, Oscar; Romero-Pérez, Julio-Ariel

Tuning procedure for event-based PI controllers under regular quantization with hysteresis. (English) Zbl 1465.93144

J. Franklin Inst. 358, No. 9, 4643-4670 (2021).

MSC: 93C65 93B70

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Skripnik, N. V.

Averaging method for impulsive differential inclusions with fuzzy right-hand side. (English) Zbl 1478.34023

Mat. Stud. 55, No. 1, 76-84 (2021).

Reviewer: Tatyana Komleva (Odessa)

MSC: 34A60 34A07 34A37 34C29

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Ogundele, Ayansola D.; Agboola, Olufemi A.; Sinha, Subhash C.

Mathematical modeling and simulation of nonlinear spacecraft rendezvous and formation flying problems via averaging method. (English) Zbl 1466.70037

Commun. Nonlinear Sci. Numer. Simul. 95, Article ID 105668, 17 p. (2021).

MSC: 70M20 34C29 70E55

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Rega, Giuseppe

Tribute to Ali H. Nayfeh (1933–2017). (English) Zbl 1471.01054

Kovacic, Ivana (ed.) et al., IUTAM symposium on exploiting nonlinear dynamics for engineering systems. ENOLIDES 2018. Proceedings of the IUTAM symposium, Novi Sad, Serbia, July 15–19, 2018. Cham: Springer. IUTAM Bookser. 37, 1-13 (2020).

MSC: 01A70

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Zhou, Yang; Wu, Baisheng; Lim, C. W.; Sun, Weipeng

Analytical approximations to primary resonance response of harmonically forced oscillators with strongly general nonlinearity. (English) Zbl 1481.70089

Appl. Math. Modelling 87, 534-545 (2020).

MSC: 70K30 34C15

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Smirnov, Valeri V.; Manevitch, Leonid I.

Complex envelope variable approximation in nonlinear dynamics. (English) Zbl 1470.70029

Russ. J. Nonlinear Dyn. 16, No. 3, 491-515 (2020).

MSC: 70K70 34C15 34E10 37J99

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Andrievskiĭ, Boris Rostislavich; Zaĭtseva, Yuliya Sergeevna; Kudryashova, Elena Vladimirovna; Kuznetsov, Nikolaĭ Vladimirovich; Kuznetsova, Ol’ga Aleksandrovna

Methods for pilot-induced oscillation prevention. A survey. (Russian. English summary) Zbl 1448.93237

Differ. Uravn. Protsessy Upr. 2020, No. 2, 131-172 (2020).

MSC: 93C95 93C10 93-02

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Guillot, Louis; Vergez, Christophe; Cochelin, Bruno

Continuation of periodic solutions of various types of delay differential equations using asymptotic numerical method and harmonic balance method. (English) Zbl 1430.34077

Nonlinear Dyn. 97, No. 1, 123-134 (2019).

MSC: 34K13 34K40 00A65

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Guillot, Louis; Cochelin, Bruno; Vergez, Christophe

A Taylor series-based continuation method for solutions of dynamical systems. (English) Zbl 1430.37099

Nonlinear Dyn. 98, No. 4, 2827-2845 (2019).

MSC: 37M20 34E05

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Zhang, Zhiwei; Wang, Yingjie; Wang, Wei; Tian, Ruilan

Periodic solution of the strongly nonlinear asymmetry system with the dynamic frequency method. (English) Zbl 1425.34041

Symmetry 11, No. 5, Paper No. 676, 14 p. (2019).

MSC: 34A45 34A34 34C25 34C60

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Percus, Jerome K.

Some remarks on pattern formation in vertebrate embryology. (English) Zbl 1421.35388

J. Stat. Phys. 175, No. 3-4, 725-728 (2019).

MSC: 35Q92 92C15 92D20 92C37 35B36

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Taha, Haithem; Rezaei, Amir S.

Viscous extension of potential-flow unsteady aerodynamics: the lift frequency response problem. (English) Zbl 1415.76164

J. Fluid Mech. 868, 141-175 (2019).

MSC: 76D10 76D25 76G25 76D05

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Gao, Peng

Bogoliubov averaging principle of stochastic reaction-diffusion equation. (English) Zbl 1409.60095

J. Differ. Equations 266, No. 10, 6702-6738 (2019).

Reviewer: Guanggan Chen (Chengdu)

MSC: 60H15

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Hentosh, Oksana Ye.; Kyshakevych, Bohdan Yu.; Blackmore, Denis; Prykarpatski, Anatolij K.

New fractional nonlinear integrable Hamiltonian systems. (English) Zbl 1409.37073

Appl. Math. Lett. 88, 41-49 (2019).

MSC: 37K30 37K10

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Remmi, S. K.; Latha, M. M.

Cubic quintic septic Duffing oscillator: an analytical study. (English) Zbl 07820712

Chin. J. Phys., Taipei 56, No. 5, 2085-2094 (2018).

MSC: 34C15 34A45 34C25 70K25

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Hieu, D. V.; Hai, N. Q.; Hung, D. T.

The equivalent linearization method with a weighted averaging for solving undamped nonlinear oscillators. (English) Zbl 1437.65066

J. Appl. Math. 2018, Article ID 7487851, 15 p. (2018).

MSC: 65L05 34C15

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Smirnov, V. V.; Manevitch, L. I.

Forced oscillations of the string under conditions of ‘sonic vacuum’. (English) Zbl 1404.74020

Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2127, Article ID 20170135, 14 p. (2018); correction ibid. 377, No. 2141, Article ID 20180382, 1 p. (2019).

MSC: 74B20 34C15 37N05 74H45 74K05

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Scheinker, Alexander; Scheinker, David

Constrained extremum seeking stabilization of systems not affine in control. (English) Zbl 1390.93692

Int. J. Robust Nonlinear Control 28, No. 2, 568-581 (2018).

MSC: 93D21 93C15

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Akbari, M. R.; Nimafar, M.; Ganji, D. D.; Karimi Chalmiani, H.

Investigation on non-linear vibration in arched beam for bridges construction via AGM method. (English) Zbl 1411.74025

Appl. Math. Comput. 298, 95-110 (2017).

MSC: 74H45 74K10

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Johannessen, Kim

The Duffing oscillator with damping for a softening potential. (English) Zbl 1397.34064

Int. J. Appl. Comput. Math. 3, No. 4, 3805-3816 (2017).

MSC: 34C15 34B30

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Argatov, Ivan; Iantchenko, Alexei; Kocherbitov, Vitaly

How to define the storage and loss moduli for a rheologically nonlinear material? A constructive review of nonlinear rheological measures. (English) Zbl 1392.76003

Contin. Mech. Thermodyn. 29, No. 6, 1375-1387 (2017).

MSC: 76A05 76-02

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Detroux, T.; Renson, L.; Masset, L.; Kerschen, G.

The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems. (English) Zbl 1423.70052

Comput. Methods Appl. Mech. Eng. 296, 18-38 (2015).

MSC: 70K50 37N05

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San-Juan, Juan Félix; López, Rosario; Pérez, Iván; San-Martín, Montserrat

A note about certain arbitrariness in the solution of the homological equation in Deprit’s method. (English) Zbl 1394.70047

Math. Probl. Eng. 2015, Article ID 982857, 10 p. (2015).

MSC: 70G45 37J40

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Lanusse, P.; Sabatier, J.; Oustaloup, A.

Fractional order PID and first generation CRONE control system design. (English) Zbl 1334.93085

Sabatier, Jocelyn et al., Fractional order differentiation and robust control design: CRONE, H-infinity and motion control. Dordrecht: Springer (ISBN 978-94-017-9806-8/hbk; 978-94-017-9807-5/ebook). Intelligent Systems, Control and Automation: Science and Engineering 77, 63-105 (2015).

MSC: 93C15 34A08 93C80 93D99 93B35

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Leonov, G. A.; Kuznetsov, N. V.; Yuldashev, M. V.; Yuldashev, R. V.

Mathematical models of the Costas loop. (English. Russian original) Zbl 1338.94116

Dokl. Math. 92, No. 2, 594-598 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 464, No. 6, 660-664 (2015).

MSC: 94C05

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Leonov, G. A.; Kuznetsov, N. V.; Yuldahsev, M. V.; Yuldashev, R. V.

Computation of the phase detector characteristic of classical PLL. (English. Russian original) Zbl 1354.93151

Dokl. Math. 91, No. 2, 246-249 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 461, No. 2, 151-154 (2015).

MSC: 93E10 93E11 94A12

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Heydari, M.; Loghmani, G. B.; Hosseini, S. M.

An improved piecewise variational iteration method for solving strongly nonlinear oscillators. (English) Zbl 1319.65059

Comput. Appl. Math. 34, No. 1, 215-249 (2015).

Reviewer: Ivan Secrieru (Chişinău)

MSC: 65L05 65L06 34A34

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Lara, Martin; San-Juan, Juan F.; López-Ochoa, Luis M.

Delaunay variables approach to the elimination of the perigee in artificial satellite theory. (English) Zbl 1298.70045

Celest. Mech. Dyn. Astron. 120, No. 1, 39-56 (2014).

MSC: 70M20 70-08 70G10 70F15 70G65

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Åström, Karl J.; Kumar, P. R.

Control: a perspective. (English) Zbl 1298.93013

Automatica 50, No. 1, 3-43 (2014).

MSC: 93A10 93B52

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Jenkins, Alejandro

Self-oscillation. (English) Zbl 1295.34050

Phys. Rep. 525, No. 2, 167-222 (2013).

MSC: 34C15 93B52 34C05 34D20

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Cveticanin, L.

Van der Pol oscillator with time variable parameters. (English) Zbl 1330.70079

Acta Mech. 224, No. 5, 945-955 (2013).

MSC: 70P05 70K05

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Limnios, Nikolaos; Swishchuk, Anatoliy

Discrete-time semi-Markov random evolutions and their applications. (English) Zbl 1271.90106

Adv. Appl. Probab. 45, No. 1, 214-240 (2013).

Reviewer: Laszlo Lakatos (Budapest)

MSC: 90C40 60K37 60K15 60B10 60F17

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Arefeva, I. Ya.; Bulatov, N. V.; Gorbachev, R. V.

Friedmann cosmology with nonpositive-definite Higgs potentials. (English. Russian original) Zbl 1282.83062

Theor. Math. Phys. 173, No. 1, 1466-1480 (2012); translation from Teor. Mat. Fiz. 173, No. 1, 160-176 (2012).

MSC: 83F05

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Arefeva, I. Ya.; Volovich, I. V.; Piskovskiy, E. V.

Rolling in the Higgs model and elliptic functions. (English. Russian original) Zbl 1356.70034

Theor. Math. Phys. 172, No. 1, 1001-1016 (2012); translation from Teor. Mat. Fiz. 172, No. 1, 138-154 (2012).

MSC: 70K99 37J40

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Cveticanin, L.; Kalami-Yazdi, M.; Askari, H.

Analytical approximations to the solutions for a generalized oscillator with strong nonlinear terms. (English) Zbl 1276.34009

J. Eng. Math. 77, 211-223 (2012).

MSC: 34A45 34C15

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Boiko, Igor M.

Dynamic harmonic balance principle and analysis of rocking block motions. (English) Zbl 1273.93085

J. Franklin Inst. 349, No. 3, 1198-1212 (2012).

MSC: 93C15 34K13

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Anh, N. D.; Zakovorotny, V. L.; Hieu, N. N.; Diep, D. V.

A dual criterion of stochastic linearization method for multi-degree-of-freedom systems subjected to random excitation. (English) Zbl 1307.70023

Acta Mech. 223, No. 12, 2667-2684 (2012).

MSC: 70L05

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Cveticanin, L.

Oscillator with non-integer order nonlinearity and time variable parameters. (English) Zbl 1328.70017

Acta Mech. 223, No. 7, 1417-1429 (2012).

MSC: 70K70 34C15 70H45 70K65

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Ni, Wei; Wang, Xiaoli; Xiong, Chun

Leader-following consensus of multiple linear systems under switching topologies: an averaging method. (English) Zbl 1255.93069

Kybernetika 48, No. 6, 1194-1210 (2012).

MSC: 93C15 93C35

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Cveticanin, Livija

Forced pure nonlinear symmetrical oscillators. (English) Zbl 1255.34035

Math. Comput. Modelling 55, No. 3-4, 1580-1593 (2012).

MSC: 34C15

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Hosen, Md. Alal; Rahman, M. Saifur; Alam, M. Shamsul; Amin, M. Ruhul

An analytical technique for solving a class of strongly nonlinear conservative systems. (English) Zbl 1248.34012

Appl. Math. Comput. 218, No. 9, 5474-5486 (2012).

Reviewer: Nicolae Pop (Baia Mare)

MSC: 34A45 34C25

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Jiménez-Lara, Lidia; Llibre, Jaume

Periodic orbits and nonintegrability of generalized classical Yang-Mills Hamiltonian systems. (English) Zbl 1315.70010

J. Math. Phys. 52, No. 3, 032901, 9 p. (2011).

MSC: 70S15 70S05 70H07 70S10 37C27

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Ramos, J. I.; García-López, C. M.

On two classes of autonomous third-order nonlinear ordinary differential equations. (English) Zbl 1232.34020

Appl. Math. Comput. 218, No. 5, 2011-2024 (2011).

MSC: 34A34 34A05 34C25

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Vrabel, R.; Abas, M.

Frequency control of singularly perturbed forced Duffing’s oscillator. (English) Zbl 1238.34071

J. Dyn. Control Syst. 17, No. 3, 451-467 (2011).

Reviewer: Vasile Dragan (Bucureşti)

MSC: 34C15 34E15 34C20 34A26

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Boiko, Igor M.

On frequency-domain criterion of finite-time convergence of second-order sliding mode control algorithms. (English) Zbl 1227.93082

Automatica 47, No. 9, 1969-1973 (2011).

MSC: 93C80 93B12 93C15 93C05

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Alam, M. Shamsul; Roy, Kamalesh Chandra; Rahman, M. Saifur; Hossain, Md. Mossaraf

An analytical technique to find approximate solutions of nonlinear damped oscillatory systems. (English) Zbl 1222.34015

J. Franklin Inst. 348, No. 5, 899-916 (2011).

MSC: 34A45 34C15 34C25

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Perestyuk, Mykola; Feketa, Petro

Invariant sets of impulsive differential equations with particularities in \(\omega \)-limit set. (English) Zbl 1238.34022

Abstr. Appl. Anal. 2011, Article ID 970469, 14 p. (2011).

Reviewer: Giovanni Giachetta (Camerino)

MSC: 34A37 34D35 34C45

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Cveticanin, L.; Kovacic, I.; Rakaric, Z.

Asymptotic methods for vibrations of the pure non-integer order oscillator. (English) Zbl 1205.34037

Comput. Math. Appl. 60, No. 9, 2616-2628 (2010).

MSC: 34C15

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Liao, Shijun

Notes on the homotopy analysis method: some definitions and theorems. (English) Zbl 1221.65126

Commun. Nonlinear Sci. Numer. Simul. 14, No. 4, 983-997 (2009).

MSC: 65H99 35A25 35C10

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Momani, Shaher; Erjaee, G. H.; Alnasr, M. H.

The modified homotopy perturbation method for solving strongly nonlinear oscillators. (English) Zbl 1189.65168

Comput. Math. Appl. 58, No. 11-12, 2209-2220 (2009).

MSC: 65L99

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Magal, Pierre; Ruan, Shigui

Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models. (English) Zbl 1191.35045

Mem. Am. Math. Soc. 951, 71 p. (2009).

Reviewer: Lutz Recke (Berlin)

MSC: 35B32 37L10 92D25 35L90 35F25 47D06

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Alam, M. Shamsul; Azad, M. Abul Kalam; Roy, Kamalesh Chandra; Rahman, M. Majedur

An extension of the general Struble’s method for solving an \(n\)th order nonlinear differential equation when the corresponding unperturbed equation has some repeated eigenvalues. (English) Zbl 1173.34002

J. Franklin Inst. 346, No. 2, 112-125 (2009).

Reviewer: Cemil Tunç (Van)

MSC: 34A34

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Bright, Ido

Tight estimates for general averaging applied to almost-periodic differential equations. (English) Zbl 1179.34041

J. Differ. Equations 246, No. 7, 2922-2937 (2009).

Reviewer: Xiaoping Yuan (Shanghai)

MSC: 34C29 34C27

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Momani, Shaher; Ertürk, Vedat Suat

Solutions of nonlinear oscillators by the modified differential transform method. (English) Zbl 1142.65058

Comput. Math. Appl. 55, No. 4, 833-842 (2008).

MSC: 65L05 34A34 34C15

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Socha, Leslaw

Linearization techniques in stochastic dynamic systems. (English) Zbl 1298.74120

Elishakoff, Isaac (ed.), Mechanical vibration: Where do we stand?. Wien: Springer (ISBN 978-3-211-68586-0/hbk). CISM Courses and Lectures 488, 249-319 (2007).

MSC: 74H50 70L05 74-02 70-02

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Hacıefendioğlu, Kemal; Başağa, Hasan Basri; Bayraktar, Alemdar; Ateş, şevket

Nonlinear analysis of rock-fill dams to non-stationary excitation by the stochastic Wilson-\(\theta \) method. (English) Zbl 1193.86005

Appl. Math. Comput. 194, No. 2, 333-345 (2007).

MSC: 86A15 65M60 74H50 86A17

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Dai, L.; Xu, L.; Dong, M.

Assessment of the behavior of weakly and highly nonlinear friction-driven oscillatory systems. (English) Zbl 1064.34023

Commun. Nonlinear Sci. Numer. Simul. 10, No. 1, 57-71 (2005).

Reviewer: Mohan Lal Mehra (Bonn)

MSC: 34C15 70F40 34A34

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Sinou, J.-J.; Thouverex, F.; Jézéquel, L.

Methods to reduce nonlinear mechanical systems for instability computation. (English) Zbl 1078.70002

Arch. Comput. Methods Eng. 11, No. 3, 257-344 (2004).

MSC: 70-08 70K20 74H15 74H45 74K99

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Momani, Shaher

Analytical approximate solutions of nonlinear oscillators by the modified decomposition method. (English) Zbl 1119.65356

Int. J. Mod. Phys. C 15, No. 7, 967-979 (2004).

MSC: 65L06

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Lim, C. W.; Wu, B. S.

A new analytical approach to the Duffing-harmonic oscillator. (English) Zbl 1055.70009

Phys. Lett., A 311, No. 4-5, 365-373 (2003).

MSC: 70K42

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Aubin, David; Dalmedico, Amy Dahan

Writing the history of dynamical systems and chaos: ‘Longue durée’ and revolution, disciplines and cultures. (English) Zbl 1026.01014

Hist. Math. 29, No. 3, 273-339 (2002).

Reviewer: Cristina Irimia (Iasi)

MSC: 01A60 01A85 37-03 76-03 82-03 86-03

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Alam, M. Shamsul

A unified Krylov-Bogoliubov-Mitropolskii method for solving \(n\)th order nonlinear systems. (English) Zbl 1019.93022

J. Franklin Inst. 339, No. 2, 239-248 (2002).

MSC: 93C10 93B51

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Nizette, Michel; Erneux, Thomas; Gavrielides, Athanasios; Kovanis, Vassilios

Averaged equations for injection locked semiconductor lasers. (English) Zbl 0987.81120

Physica D 161, No. 3-4, 220-236 (2002).

MSC: 81V80 82D37

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Belhaq, M.; Lakrad, F.

Prediction of homoclinic bifurcation: the elliptic averaging method. (English) Zbl 0953.34026

Chaos Solitons Fractals 11, No. 14, 2251-2258 (2000).

MSC: 34C23 34C37 34C15 34C29

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Lehman, Brad; Weibel, Steven P.

Fundamental theorems of averaging for functional differential equations. (English) Zbl 0930.34044

J. Differ. Equations 152, No. 1, 160-190 (1999).

Reviewer: Marcos Lizana (Merida)

MSC: 34K05 34C29

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Ispolov, Yu. G.; Smolnikov, B. A.

Skateboard dynamics. (English) Zbl 0900.70109

Comput. Methods Appl. Mech. Eng. 131, No. 3-4, 327-333 (1996).

MSC: 70E15 70F25 92C10 70E60

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Elnagar, A. M.; El-Bassiouny, A. F.

Response of self-excited three-degree-of-freedom systems to multifrequency excitations. (English) Zbl 0760.70014

Int. J. Theor. Phys. 31, No. 8, 1531-1548 (1992).

MSC: 70K30 70K20 70K40

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Krenz, G. S.; Miller, R. K.

Stability analysis of almost sinusoidal periodic oscillations in nonlinear control systems subjected to nonconstant periodic input. (English) Zbl 0767.93070

J. Integral Equations Appl. 2, No. 4, 595-613 (1990).

MSC: 93D05 93C10 93C73

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Cheng, Shuili; Tan, Zhimin

Defect and improvement of two-time expansion method in nonlinear oscillations. (English) Zbl 0850.70254

Appl. Math. Mech., Engl. Ed. 10, No. 10, 915-924 (1989).

MSC: 70K99

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Watanabe, Hisao

Averaging and fluctuations for parabolic equations with rapidly oscillating random coefficients. (English) Zbl 0682.60047

Probab. Theory Relat. Fields 77, No. 3, 359-378 (1988).

MSC: 60H15

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Sattar, M. A.

An asymptotic method for second-order critically damped nonliner equations. (English) Zbl 0593.34037

J. Franklin Inst. 321, 109-113 (1986).

Reviewer: P.Marusciak

MSC: 34C10 34A34

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Koniges, A. E.; Johnson, J. L.

A helical axis stellarator equilibrium model. (English) Zbl 0588.76195

Phys. Fluids 28, 3127-3135 (1985).

MSC: 76W05

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Liu, Jong C.

The uniqueness of normal forms via Lie transforms and its applications to Hamiltonian systems. (English) Zbl 0581.70009

Celestial Mech. 36, 89-104 (1985).

Reviewer: Y.Kozai

MSC: 70H05 70F07

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McConnell, James

Debye limit of the stochastic rotation operator. (English) Zbl 0599.60098

Physica A 128, 611-630 (1984).

MSC: 60K35 81P20

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Bojadziev, G. N.

Damped nonlinear oscillations modeled by a 3-dimensional differential system. (English) Zbl 0527.70028

Acta Mech. 48, 193-201 (1983).

MSC: 70K99

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Thompson, J. M. T.; Lunn, T. S.

Resonance-sensitivity in dynamic Hopf bifurcations under fluid loading. (English) Zbl 0489.73053

Appl. Math. Modelling 5, 143-150 (1981).

MSC: 74H55 74F10

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Arya, J. C.; Bojadziev, G. N.

Time-dependent oscillating systems with damping, slowly varying parameters, and delay. (English) Zbl 0462.70016

Acta Mech. 41, 109-119 (1981).

MSC: 70K99

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Tsyganovskij, N. S.

Justification of the method of averaging for systems with pulsed action. (English) Zbl 0468.34029

Ukr. Math. J. 31, 376-379 (1980).

MSC: 34C29

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Bojadziev, G. N.

Damped oscillating processes in biological and biochemical systems. (English) Zbl 0443.92005

Bull. Math. Biol. 42, 701-718 (1980).

MSC: 92Cxx 92B05 92D25 92Exx 80A30 34C15 34E10

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Atherton, D. P.; Dorrah, H. T.

A survey on non-linear oscillations. (English) Zbl 0438.34029

Int. J. Control 31, 1041-1105 (1980).

MSC: 34C15 70Kxx 93C10

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Arya, J. C.; Bojadziev, G. N.

Damped oscillating systems modeled by hyperbolic differential equations with slowly varying coefficients. (English) Zbl 0423.35012

Acta Mech. 35, 215-221 (1980).

MSC: 35B05 35Q99 35L99

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Bojadziev, G.; Chan, S.

Asymptotic solutions of differential equations with time delay in population dynamics. (English) Zbl 0402.92024

Bull. Math. Biol. 41, 325-342 (1979).

MSC: 92D25 34K99

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Linkens, D. A.

The method of harmonic balance applied to coupled asymmetrical van der Pol oscillators for intestinal modelling. (English) Zbl 0402.92014

Bull. Math. Biol. 41, 573-589 (1979).

MSC: 92Cxx 92B05

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Arya, J. C.

The effect of kinematical non-linearities on the vibration frequencies of a damped string. (English) Zbl 0401.70022

Acta Mech. 29, 159-167 (1978).

MSC: 70K99 74H45 41A60 35L10

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Lardner, R. W.; Bojadziev, G. N.

Vibrations of a viscoelastic rod with small non-linearities. (English) Zbl 0412.35003

Meccanica 12, 249-256 (1977).

MSC: 35A25 35L99 74H45

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Balachandra, M.

An averaging theorem for two-point boundary value problems with applications to optimal control. (English) Zbl 0346.34029

J. Math. Anal. Appl. 55, 46-60 (1976).

MSC: 34C30 34B15 49K15

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Dutt, Ranabir; Ghosh, P. K.

Nonlinear correction to Lotka-Volterra oscillation in a prey-predator system. (English) Zbl 0318.92011

Math. Biosci. 27, 9-16 (1975).

MSC: 92B05 34D10 34A99

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Murdock, James A.

Resonance capture in certain nearly Hamiltonian systems. (English) Zbl 0274.70014

J. Differ. Equations 17, 361-374 (1975).

MSC: 70K99 34C25 70F15 70M20

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Found 107 Documents (Results 1–100)

Quasiperiodic birhythmicity in a multicycle van der Pol oscillator. (English) Zbl 07920641

Experimental tuning of PI controllers with symmetric send-on-delta sampling from the step response. (English) Zbl 1533.93214

Strong and weak convergence for the averaging principle of DDSDE with singular drift. (English) Zbl 07824115

Exact time-integral inversion via Čebyšëv quintic approximations for nonlinear oscillators. (English) Zbl 1540.34078

Circuit analysis using monotone+skew splitting. (English) Zbl 1530.94075

Averaging principle for stochastic complex Ginzburg-Landau equations. (English) Zbl 1517.35218

The second Bogolyubov theorem and global averaging principle for SPDEs with monotone coefficients. (English) Zbl 1518.70024

When does the method of harmonic balance give a correct prediction for mechanical systems? (English) Zbl 1517.37089

A hysteretic model of localized frictional contacts with instrumental stiffness. (English) Zbl 1528.74082

Spherical model with Dzyaloshinskii-Moriya interactions. (English) Zbl 1539.82061

Permanent variational wave functions for bosons. (English) Zbl 1494.82030

Averaging principle on infinite intervals for stochastic ordinary differential equations with Lévy noise. (English) Zbl 1484.60063

Tuning procedure for event-based PI controllers under regular quantization with hysteresis. (English) Zbl 1465.93144

Averaging method for impulsive differential inclusions with fuzzy right-hand side. (English) Zbl 1478.34023

Mathematical modeling and simulation of nonlinear spacecraft rendezvous and formation flying problems via averaging method. (English) Zbl 1466.70037

Tribute to Ali H. Nayfeh (1933–2017). (English) Zbl 1471.01054

Analytical approximations to primary resonance response of harmonically forced oscillators with strongly general nonlinearity. (English) Zbl 1481.70089

Complex envelope variable approximation in nonlinear dynamics. (English) Zbl 1470.70029

Methods for pilot-induced oscillation prevention. A survey. (Russian. English summary) Zbl 1448.93237

Continuation of periodic solutions of various types of delay differential equations using asymptotic numerical method and harmonic balance method. (English) Zbl 1430.34077

A Taylor series-based continuation method for solutions of dynamical systems. (English) Zbl 1430.37099

Periodic solution of the strongly nonlinear asymmetry system with the dynamic frequency method. (English) Zbl 1425.34041

Some remarks on pattern formation in vertebrate embryology. (English) Zbl 1421.35388

Viscous extension of potential-flow unsteady aerodynamics: the lift frequency response problem. (English) Zbl 1415.76164

Bogoliubov averaging principle of stochastic reaction-diffusion equation. (English) Zbl 1409.60095

New fractional nonlinear integrable Hamiltonian systems. (English) Zbl 1409.37073

Cubic quintic septic Duffing oscillator: an analytical study. (English) Zbl 07820712

The equivalent linearization method with a weighted averaging for solving undamped nonlinear oscillators. (English) Zbl 1437.65066

Forced oscillations of the string under conditions of ‘sonic vacuum’. (English) Zbl 1404.74020

Constrained extremum seeking stabilization of systems not affine in control. (English) Zbl 1390.93692

Investigation on non-linear vibration in arched beam for bridges construction via AGM method. (English) Zbl 1411.74025

The Duffing oscillator with damping for a softening potential. (English) Zbl 1397.34064

How to define the storage and loss moduli for a rheologically nonlinear material? A constructive review of nonlinear rheological measures. (English) Zbl 1392.76003

The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems. (English) Zbl 1423.70052

A note about certain arbitrariness in the solution of the homological equation in Deprit’s method. (English) Zbl 1394.70047

Fractional order PID and first generation CRONE control system design. (English) Zbl 1334.93085

Mathematical models of the Costas loop. (English. Russian original) Zbl 1338.94116

Computation of the phase detector characteristic of classical PLL. (English. Russian original) Zbl 1354.93151

An improved piecewise variational iteration method for solving strongly nonlinear oscillators. (English) Zbl 1319.65059

Delaunay variables approach to the elimination of the perigee in artificial satellite theory. (English) Zbl 1298.70045

Control: a perspective. (English) Zbl 1298.93013

Self-oscillation. (English) Zbl 1295.34050

Van der Pol oscillator with time variable parameters. (English) Zbl 1330.70079

Discrete-time semi-Markov random evolutions and their applications. (English) Zbl 1271.90106

Friedmann cosmology with nonpositive-definite Higgs potentials. (English. Russian original) Zbl 1282.83062

Rolling in the Higgs model and elliptic functions. (English. Russian original) Zbl 1356.70034

Analytical approximations to the solutions for a generalized oscillator with strong nonlinear terms. (English) Zbl 1276.34009

Dynamic harmonic balance principle and analysis of rocking block motions. (English) Zbl 1273.93085

A dual criterion of stochastic linearization method for multi-degree-of-freedom systems subjected to random excitation. (English) Zbl 1307.70023

Oscillator with non-integer order nonlinearity and time variable parameters. (English) Zbl 1328.70017

Leader-following consensus of multiple linear systems under switching topologies: an averaging method. (English) Zbl 1255.93069

Forced pure nonlinear symmetrical oscillators. (English) Zbl 1255.34035

An analytical technique for solving a class of strongly nonlinear conservative systems. (English) Zbl 1248.34012

Periodic orbits and nonintegrability of generalized classical Yang-Mills Hamiltonian systems. (English) Zbl 1315.70010

On two classes of autonomous third-order nonlinear ordinary differential equations. (English) Zbl 1232.34020

Frequency control of singularly perturbed forced Duffing’s oscillator. (English) Zbl 1238.34071

On frequency-domain criterion of finite-time convergence of second-order sliding mode control algorithms. (English) Zbl 1227.93082

An analytical technique to find approximate solutions of nonlinear damped oscillatory systems. (English) Zbl 1222.34015

Invariant sets of impulsive differential equations with particularities in \(\omega \)-limit set. (English) Zbl 1238.34022

Asymptotic methods for vibrations of the pure non-integer order oscillator. (English) Zbl 1205.34037

Notes on the homotopy analysis method: some definitions and theorems. (English) Zbl 1221.65126

The modified homotopy perturbation method for solving strongly nonlinear oscillators. (English) Zbl 1189.65168

Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models. (English) Zbl 1191.35045

An extension of the general Struble’s method for solving an \(n\)th order nonlinear differential equation when the corresponding unperturbed equation has some repeated eigenvalues. (English) Zbl 1173.34002

Tight estimates for general averaging applied to almost-periodic differential equations. (English) Zbl 1179.34041

Solutions of nonlinear oscillators by the modified differential transform method. (English) Zbl 1142.65058

Linearization techniques in stochastic dynamic systems. (English) Zbl 1298.74120

Nonlinear analysis of rock-fill dams to non-stationary excitation by the stochastic Wilson-\(\theta \) method. (English) Zbl 1193.86005

Assessment of the behavior of weakly and highly nonlinear friction-driven oscillatory systems. (English) Zbl 1064.34023

Methods to reduce nonlinear mechanical systems for instability computation. (English) Zbl 1078.70002

Analytical approximate solutions of nonlinear oscillators by the modified decomposition method. (English) Zbl 1119.65356

A new analytical approach to the Duffing-harmonic oscillator. (English) Zbl 1055.70009

Writing the history of dynamical systems and chaos: ‘Longue durée’ and revolution, disciplines and cultures. (English) Zbl 1026.01014

A unified Krylov-Bogoliubov-Mitropolskii method for solving \(n\)th order nonlinear systems. (English) Zbl 1019.93022