Wang, Yu; Cao, Jinde; Kurths, Jürgen; Yanchuk, Serhiy Universal bifurcation scenarios in delay-differential equations with one delay. (English) Zbl 07903641 J. Differ. Equations 406, 366-396 (2024). Reviewer: Neville J. Ford (Chester) MSC: 34K18 34K21 34K20 34K08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Berezansky, Leonid; Braverman, Elena On stability of equations with an infinite distributed delay. (English) Zbl 07867503 Nonlinearity 37, No. 6, Article ID 065022, 21 p. (2024). MSC: 34K20 34K25 92D25 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Breda, Dimitri; Liessi, Davide; Verduyn Lunel, Sjoerd M. Spectra of evolution operators of a class of neutral renewal equations: theoretical and numerical aspects. (English) Zbl 07856357 Appl. Numer. Math. 200, 124-137 (2024). MSC: 47Dxx 65J08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Faria, Teresa Asymptotic behaviour of general nonautonomous Nicholson equations with mixed monotonicities. (English) Zbl 07835875 Nonlinear Anal., Real World Appl. 77, Article ID 104044, 16 p. (2024). Reviewer: Genghong Lin (Guangzhou) MSC: 34K60 92D25 37C60 34K25 34K13 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Toprakseven, Şuayip; Tao, Xia; Hao, Jiaxiong Error analysis of a weak Galerkin finite element method for singularly perturbed differential-difference equations. (English) Zbl 07827783 J. Difference Equ. Appl. 30, No. 4, 435-464 (2024). MSC: 65L03 × Cite Format Result Cite Review PDF Full Text: DOI
Ayele, Mulunesh Amsalu; Tiruneh, Awoke Andargie; Derese, Getachew Adamu Fitted cubic spline scheme for two-parameter singularly perturbed time-delay parabolic problems. (English) Zbl 1518.65081 Results Appl. Math. 18, Article ID 100361, 17 p. (2023). MSC: 65M06 65D07 65M12 65M15 65M22 35B25 35R07 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Garima; Sharma, Kapil K. Parameter uniform fitted mesh finite difference scheme for elliptical singularly perturbed problems with mixed shifts in two dimensions. (English) Zbl 1524.65712 Int. J. Comput. Math. 100, No. 6, 1264-1283 (2023). MSC: 65N06 65N22 35J25 39A06 39A14 35B25 65N15 41A58 × Cite Format Result Cite Review PDF Full Text: DOI
Khari, Kartikay; Kumar, Vivek Finite element analysis of the singularly perturbed parabolic reaction-diffusion problems with retarded argument. (English) Zbl 1533.65173 Numer. Methods Partial Differ. Equations 38, No. 4, 997-1014 (2022). MSC: 65M60 65M06 65N30 65N50 65M80 65M12 65M15 35B25 35R07 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Xue; Scarabel, Francesca; Wang, Xiang-Sheng; Wu, Jianhong Global continuation of periodic oscillations to a diapause rhythm. (English) Zbl 1510.34151 J. Dyn. Differ. Equations 34, No. 4, 2819-2839 (2022). Reviewer: Changjin Xu (Guiyang) MSC: 34K13 34K18 34K60 92D25 × Cite Format Result Cite Review PDF Full Text: DOI
Yanchuk, Serhiy; Wolfrum, Matthias; Pereira, Tiago; Turaev, Dmitry Absolute stability and absolute hyperbolicity in systems with discrete time-delays. (English) Zbl 1494.34165 J. Differ. Equations 318, 323-343 (2022). Reviewer: Jun Zhou (Chengdu) MSC: 34K20 34K06 34K08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, Shu-Bo; Soradi-Zeid, Samaneh; Dutta, Hemen; Mesrizadeh, Mehdi; Jahanshahi, Hadi; Chu, Yu-Ming Reproducing kernel Hilbert space method for nonlinear second order singularly perturbed boundary value problems with time-delay. (English) Zbl 1498.34063 Chaos Solitons Fractals 144, Article ID 110674, 10 p. (2021). MSC: 34A45 34E15 × Cite Format Result Cite Review PDF Full Text: DOI
Podila, Pramod Chakravarthy; Gupta, Trun A nonstandard method for a coupled system of singularly perturbed delay differential equations. (English) Zbl 1499.34378 Int. J. Appl. Comput. Math. 7, No. 3, Paper No. 105, 11 p. (2021). MSC: 34K26 34K10 34K06 65L03 × Cite Format Result Cite Review PDF Full Text: DOI
Chakravarthy, P. Pramod; Kumar, Kamalesh A novel method for singularly perturbed delay differential equations of reaction-diffusion type. (English) Zbl 1483.65109 Differ. Equ. Dyn. Syst. 29, No. 3, 723-734 (2021). MSC: 65L03 34K26 65L10 65L11 × Cite Format Result Cite Review PDF Full Text: DOI
Mazanti, Guilherme; Boussaada, Islam; Niculescu, Silviu-Iulian Multiplicity-induced-dominancy for delay-differential equations of retarded type. (English) Zbl 1471.34140 J. Differ. Equations 286, 84-118 (2021). Reviewer: Nikita V. Artamonov (Moskva) MSC: 34K20 34K06 34K35 93D15 33C90 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Touaoula, Tarik Mohammed; Frioui, Mohammed Nor; Bessonov, Nikolay; Volpert, Vitaly Dynamics of solutions of a reaction-diffusion equation with delayed inhibition. (English) Zbl 1450.35143 Discrete Contin. Dyn. Syst., Ser. S 13, No. 9, 2425-2442 (2020). MSC: 35K57 35K20 35R10 92C37 35B41 35B36 × Cite Format Result Cite Review PDF Full Text: DOI
Liz, Eduardo Clark’s equation: a useful difference equation for population models, predictive control, and numerical approximations. (English) Zbl 1448.37122 Qual. Theory Dyn. Syst. 19, No. 2, Paper No. 71, 11 p. (2020). MSC: 37N25 39A60 39A30 92D25 × Cite Format Result Cite Review PDF Full Text: DOI
Braverman, Elena; Hasik, Karel; Ivanov, Anatoli F.; Trofimchuk, Sergei I. A cyclic system with delay and its characteristic equation. (English) Zbl 1484.34161 Discrete Contin. Dyn. Syst., Ser. S 13, No. 1, 1-29 (2020). Reviewer: Serhiy Yanchuk (Berlin) MSC: 34K25 34K11 34K20 34K06 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Touaoula, Tarik Mohammed Global dynamics for a class of reaction-diffusion equations with distributed delay and Neumann condition. (English) Zbl 1439.35512 Commun. Pure Appl. Anal. 19, No. 5, 2473-2490 (2020). MSC: 35R10 35B40 35Q92 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liz, Eduardo; Buedo-Fernández, Sebastián A new formula to get sharp global stability criteria for one-dimensional discrete-time models. (English) Zbl 1429.39010 Qual. Theory Dyn. Syst. 18, No. 3, 813-824 (2019). MSC: 39A30 39A10 34K20 × Cite Format Result Cite Review PDF Full Text: DOI Link
Chakravarthy, P. Pramod; Gupta, Trun; Rao, R. Nageshwar A numerical scheme for singularly perturbed delay differential equations of convection-diffusion type on an adaptive grid. (English) Zbl 1488.65158 Math. Model. Anal. 23, No. 4, 686-698 (2018). MSC: 65L03 65L10 65L11 65L12 65L20 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Touaoula, Tarik Mohammed Global stability for a class of functional differential equations (application to Nicholson’s blowflies and Mackey-Glass models). (English) Zbl 1398.34102 Discrete Contin. Dyn. Syst. 38, No. 9, 4391-4419 (2018). Reviewer: Leonid Berezanski (Beer-Sheva) MSC: 34K20 92D25 × Cite Format Result Cite Review PDF Full Text: DOI
Pramod Chakravarthy, P.; Dinesh Kumar, S.; Nageshwar Rao, R. Numerical solution of second order singularly perturbed delay differential equations via cubic spline in tension. (English) Zbl 1397.65027 Int. J. Appl. Comput. Math. 3, No. 3, 1703-1717 (2017). MSC: 65D07 65L03 92-08 × Cite Format Result Cite Review PDF Full Text: DOI
Kumar, Sunil; Kumar, Mukesh A second order uniformly convergent numerical scheme for parameterized singularly perturbed delay differential problems. (English) Zbl 1382.65211 Numer. Algorithms 76, No. 2, 349-360 (2017). Reviewer: Raffaella Pavani (Milano) MSC: 65L11 65L10 34K26 65L50 65L12 65L70 65L03 65L20 × Cite Format Result Cite Review PDF Full Text: DOI
Chow, Shui-Nee; Nussbaum, Roger D.; Walther, Hans-Otto John Mallet-Paret 60. (English) Zbl 1348.01017 J. Dyn. Differ. Equations 28, No. 3-4, 595-603 (2016). MSC: 01A70 × Cite Format Result Cite Review PDF Full Text: DOI
Sa Ngiamsunthorn, Parinya Existence of periodic solutions for differential equations with multiple delays under dichotomy condition. (English) Zbl 1422.34203 Adv. Difference Equ. 2015, Paper No. 259, 11 p. (2015). MSC: 34K13 47H10 47N20 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Pramod Chakravarthy, Podila; Dinesh Kumar, S.; Nageshwar Rao, Ragi; Ghate, Devendra P. A fitted numerical scheme for second order singularly perturbed delay differential equations via cubic spline in compression. (English) Zbl 1422.34213 Adv. Difference Equ. 2015, Paper No. 300, 14 p. (2015). MSC: 34K28 65L10 34K26 34K10 65L12 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Yanchuk, Serhiy; Lücken, Leonhard; Wolfrum, Matthias; Mielke, Alexander Spectrum and amplitude equations for scalar delay-differential equations with large delay. (English) Zbl 1312.34100 Discrete Contin. Dyn. Syst. 35, No. 1, 537-553 (2015). Reviewer: Giselle A. Monteiro (Prague) MSC: 34K08 34K20 34K25 34K18 34K06 × Cite Format Result Cite Review PDF Full Text: DOI
Zhao, Junsheng; Li, Yongmin; Yu, Xingjiang; Zhang, Xingfang Levenberg-Marquardt algorithm for Mackey-Glass chaotic time series prediction. (English) Zbl 1419.62264 Discrete Dyn. Nat. Soc. 2014, Article ID 193758, 6 p. (2014). MSC: 62M20 62M10 68T05 37M10 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Kumar, Sunil Layer-adapted methods for quasilinear singularly perturbed delay differential problems. (English) Zbl 1337.65096 Appl. Math. Comput. 233, 214-221 (2014). MSC: 65L11 65L03 34K26 × Cite Format Result Cite Review PDF Full Text: DOI
Zarin, Helena On discontinuous Galerkin finite element method for singularly perturbed delay differential equations. (English) Zbl 1314.65089 Appl. Math. Lett. 38, 27-32 (2014). MSC: 65L03 65L60 65L50 34K28 34K26 × Cite Format Result Cite Review PDF Full Text: DOI
Liz, Eduardo; Ruiz-Herrera, Alfonso Attractivity, multistability, and bifurcation in delayed Hopfield’s model with non-monotonic feedback. (English) Zbl 1291.34121 J. Differ. Equations 255, No. 11, 4244-4266 (2013); addendum ibid. 257, No. 4, 1307-1309 (2014). Reviewer: Angela Slavova (Sofia) MSC: 34K25 34K18 34K20 37C70 92B20 × Cite Format Result Cite Review PDF Full Text: DOI
Erdogan, Fevzi; Amiraliyev, Gabil M. Fitted finite difference method for singularly perturbed delay differential equations. (English) Zbl 1236.65098 Numer. Algorithms 59, No. 1, 131-145 (2012). Reviewer: Răzvan Răducanu (Iaşi) MSC: 65L12 65L03 65L11 65L05 65L20 65L70 34K06 34K26 34K28 × Cite Format Result Cite Review PDF Full Text: DOI
Cai, Mingshan; Xiong, Wanmin Convergence for Hopfield neural networks with state-dependent delays. (English) Zbl 1238.93043 Nonlinear Anal., Hybrid Syst. 5, No. 3, 407-412 (2011). MSC: 93C15 93C10 92B20 × Cite Format Result Cite Review PDF Full Text: DOI
Erdogan, Fevzi A parameter robust method for singularly perturbed delay differential equations. (English) Zbl 1198.65106 J. Inequal. Appl. 2010, Article ID 325654, 14 p. (2010). MSC: 65L03 65L05 65L50 65L12 65L20 34K28 34K26 × Cite Format Result Cite Review PDF Full Text: DOI EuDML OA License
Amiraliyeva, I. G.; Erdogan, F.; Amiraliyev, G. M. A uniform numerical method for dealing with a singularly perturbed delay initial value problem. (English) Zbl 1207.65091 Appl. Math. Lett. 23, No. 10, 1221-1225 (2010). Reviewer: M. Gousidou-Koutita (Thessaloniki) MSC: 65L05 34K26 65L03 34K28 65L20 × Cite Format Result Cite Review PDF Full Text: DOI
Liz, Eduardo; Röst, Gergely Dichotomy results for delay differential equations with negative Schwarzian derivative. (English) Zbl 1207.34093 Nonlinear Anal., Real World Appl. 11, No. 3, 1422-1430 (2010). Reviewer: Yuri V. Rogovchenko (Umeå) MSC: 34K25 34K19 34K12 34D09 34D45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ivanov, Anatoli F.; Trofimchuk, Sergei I. Periodic solutions of a discretized differential delay equation. (English) Zbl 1194.34129 J. Difference Equ. Appl. 16, No. 2-3, 157-171 (2010). Reviewer: Zhiming Guo (Ontario) MSC: 34K13 34K26 37E05 × Cite Format Result Cite Review PDF Full Text: DOI Link
Amiraliyev, Gabil M.; Erdogan, Fevzi A finite difference scheme for a class of singularly perturbed initial value problems for delay differential equations. (English) Zbl 1206.65191 Numer. Algorithms 52, No. 4, 663-675 (2009). Reviewer: Ziwen Jiang (Shandong) MSC: 65L12 65L11 34K26 34K28 65L20 65L50 65L70 65L05 × Cite Format Result Cite Review PDF Full Text: DOI
Amiraliyeva, I. G.; Amiraliyev, G. M. Uniform difference method for parameterized singularly perturbed delay differential equations. (English) Zbl 1206.65192 Numer. Algorithms 52, No. 4, 509-521 (2009). Reviewer: Ziwen Jiang (Shandong) MSC: 65L12 65L11 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Kempf, Roland Dynamics of functions with piecewise non-positive Schwarzian derivatives. (English) Zbl 1177.37044 J. Difference Equ. Appl. 15, No. 6, 541-556 (2009). Reviewer: Anne Broise-Alamichel (Orsay) MSC: 37E05 34L30 34D20 34K20 34D45 34K23 × Cite Format Result Cite Review PDF Full Text: DOI
Song, Yongli; Peng, Yahong; Wei, Junjie Bifurcations for a predator-prey system with two delays. (English) Zbl 1132.34053 J. Math. Anal. Appl. 337, No. 1, 466-479 (2008). Reviewer: Yuming Chen (Waterloo) MSC: 34K18 34K13 34K60 92D25 × Cite Format Result Cite Review PDF Full Text: DOI
Amiraliyev, G. M.; Erdogan, F. Uniform numerical method for singularly perturbed delay differential equations. (English) Zbl 1134.65042 Comput. Math. Appl. 53, No. 8, 1251-1259 (2007). Reviewer: Vladimir Gorbunov (Ul’yanovsk) MSC: 65L05 65L12 65L50 34K28 65L20 34K06 × Cite Format Result Cite Review PDF Full Text: DOI
Röst, Gergely; Wu, Jianhong Domain-decomposition method for the global dynamics of delay differential equations with unimodal feedback. (English) Zbl 1137.34038 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 463, No. 2086, 2655-2669 (2007). Reviewer: Eva Sanchez (Madrid) MSC: 34K25 34K60 34K28 × Cite Format Result Cite Review PDF Full Text: DOI
Kang, Shu-Gui; Zhang, Guang; Shi, Bao Existence of three periodic positive solutions for a class of integral equations with parameters. (English) Zbl 1104.45006 J. Math. Anal. Appl. 323, No. 1, 654-665 (2006). Reviewer: Kun Soo Chang (Seoul) MSC: 45N05 45M15 45M20 45G10 × Cite Format Result Cite Review PDF Full Text: DOI
Kang, Shugui; Zhang, Guang Existence of nontrivial periodic solutions for first order functional differential equations. (English) Zbl 1075.34064 Appl. Math. Lett. 18, No. 1, 101-107 (2005). MSC: 34K13 × Cite Format Result Cite Review PDF Full Text: DOI
Fan, Meng; Zou, Xingfu Global asymptotic stability of a class of nonautonomous integro-differential systems and applications. (English) Zbl 1058.45004 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 57, No. 1, 111-135 (2004). Reviewer: Mouffak Benchohra (Sidi Bel Abbes) MSC: 45J05 45G15 45M10 92B20 92D25 × Cite Format Result Cite Review PDF Full Text: DOI
Mallet-Paret, John; Nussbaum, Roger D. Boundary layer phenomena for differential-delay equations with state-dependent time lags: III. (English) Zbl 1035.34089 J. Differ. Equations 189, No. 2, 640-692 (2003). Reviewer: Yuan Rong (Beijing) MSC: 34K26 34K13 × Cite Format Result Cite Review PDF Full Text: DOI
Bartha, Mária Periodic solutions for differential equations with state-dependent delay and positive feedback. (English) Zbl 1028.34062 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 53, No. 6, 839-857 (2003). Reviewer: Meng Fan (Changchun) MSC: 34K13 × Cite Format Result Cite Review PDF Full Text: DOI
Bartha, Mária Convergence of solutions for an equation with state-dependent delay. (English) Zbl 0980.34074 J. Math. Anal. Appl. 254, No. 2, 410-432 (2001). Reviewer: Marcos Lizana (Merida) MSC: 34K25 34K07 × Cite Format Result Cite Review PDF Full Text: DOI
Huang, Wenzhang Stability of square wave periodic solution for singularly perturbed delay differential equations. (English) Zbl 0980.34073 J. Differ. Equations 168, No. 2, 239-269 (2000). Reviewer: Marcos Lizana (Merida) MSC: 34K23 34K26 × Cite Format Result Cite Review PDF Full Text: DOI Link
Mischaikow, K. (ed.); Yi, Yingfei (ed.) Special issue in celebration of Jack K. Hale’s 70th birthday. Part 2 of 4 parts. (English) Zbl 0969.00109 J. Differ. Equations 168, No. 2, 239-478 (2000). MSC: 00B30 34-06 35-06 × Cite Format Result Cite Review PDF Full Text: DOI
Cooke, Kenneth L.; Ivanov, Anatoli F. On the discretization of a delay differential equation. (English) Zbl 0954.39003 J. Difference Equ. Appl. 6, No. 1, 105-119 (2000). Reviewer: Klaus R.Schneider (Berlin) MSC: 39A11 39A12 34K13 34K26 × Cite Format Result Cite Review PDF Full Text: DOI
Huang, Wenzhang Monotonicity of heteroclinic orbits and spectral properties of variational equations for delay differential equations. (English) Zbl 0954.34071 J. Differ. Equations 162, No. 1, 91-139 (2000). Reviewer: W.M.Oliva (Lisboa) MSC: 34K25 34K13 × Cite Format Result Cite Review PDF Full Text: DOI
Wu, J.; Faria, T.; Huang, Y. S. Synchronization and stable phase-locking in a network of neurons with memory. (English) Zbl 1043.92500 Math. Comput. Modelling 30, No. 1-2, 117-138 (1999). MSC: 92B20 92C20 34K60 × Cite Format Result Cite Review PDF Full Text: DOI
Ruan, Shigui; Wei, Junjie Periodic solutions of planar systems with two delays. (English) Zbl 0946.34062 Proc. R. Soc. Edinb., Sect. A, Math. 129, No. 5, 1017-1032 (1999). Reviewer: Klaus R.Schneider (Berlin) MSC: 34K13 34K18 92B20 × Cite Format Result Cite Review PDF Full Text: DOI
Giannakopoulos, Fotios; Zapp, Andreas Local and global Hopf bifurcation in a scalar delay differential equation. (English) Zbl 1126.34371 J. Math. Anal. Appl. 237, No. 2, 425-450 (1999). MSC: 34K18 37G15 × Cite Format Result Cite Review PDF Full Text: DOI Link
Wu, Jianhong Global continua of periodic solutions to some difference-differential equations of neutral type. (English) Zbl 0778.34054 Tôhoku Math. J., II. Ser. 45, No. 1, 67-88 (1993). Reviewer: A.Cañada (Granada) MSC: 34K99 34K40 34C25 34C23 × Cite Format Result Cite Review PDF Full Text: DOI
Kuang, Yang Global attractivity and periodic solutions in delay-differential equations related to models in physiology and population biology. (English) Zbl 0758.34065 Japan J. Ind. Appl. Math. 9, No. 2, 205-238 (1992). Reviewer: G.Karakostas (Ioannina) MSC: 34K20 34K99 34C25 92C30 92D25 × Cite Format Result Cite Review PDF Full Text: DOI
Mallet-Paret, John; Nussbaum, Roger D. Boundary layer phenomena for differential-delay equations with state- dependent time lags. I. (English) Zbl 0763.34056 Arch. Ration. Mech. Anal. 120, No. 2, 99-146 (1992). Reviewer: T.Dłotko (Katowice) MSC: 34K99 34K10 34C15 34C25 92C50 × Cite Format Result Cite Review PDF Full Text: DOI
Mallet-Paret, John Morse decompositions for delay-differential equations. (English) Zbl 0648.34082 J. Differ. Equations 72, No. 2, 270-315 (1988). Reviewer: J.Ohriska MSC: 34K99 37C70 × Cite Format Result Cite Review PDF Full Text: DOI
Mallet-Paret, John; Nussbaum, Roger D. Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation. (English) Zbl 0617.34071 Ann. Mat. Pura Appl., IV. Ser. 145, 33-128 (1986). Reviewer: M.Banks MSC: 34K25 34K99 34C25 34E15 × Cite Format Result Cite Review PDF Full Text: DOI