Found 425 Documents (Results 1–100)
Strange fractal attractors and optimal chaos of memristor-memcapacitor via non-local differentials. (English) Zbl 1525.34070
Chaotic oscillators with two types of semi-fractal equilibrium points: bifurcations, multistability, and fractal basins of attraction. (English) Zbl 1516.37038
Fractal resistive-capacitive-inductive shunted Josephson junction: theoretical investigation and microcontroller implementation. (English) Zbl 1507.82085
Complicated boundaries of the attraction basin in a class of three-dimensional polynomial systems. (English) Zbl 07847252
Characterization of fractal basins using deep convolutional neural networks. (English) Zbl 1539.68323
On fractal patterns for multi-wing hyperchaotic attractors with a mirror symmetrical structure. (English) Zbl 1516.34073
Implementation of multi-folded torus attractors via a piecewise system with a piecewise linear odd function. (English) Zbl 1515.34015
The fractal and piecewise structure of some chaotic neural networks using a generalized model. (English) Zbl 1515.34014
Chaotic behavior of modified stretch-twist-fold flow under fractal-fractional derivatives. (English) Zbl 1515.34013
Master-slave synchronization of a new fractal-fractional order quaternion-valued neural networks with time-varying delays. (English) Zbl 1506.34079
Linear and rotational fractal design for multiwing hyperchaotic systems with triangle and square shapes. (English) Zbl 1504.34139
A scaling law chaotic system. (English) Zbl 1498.37063
Sharp upper and lower bounds of the attractor dimension for 3D damped Euler-Bardina equations. (English) Zbl 1490.35273
Investigation of complex behaviour of fractal fractional chaotic attractor with Mittag-Leffler Kernel. (English) Zbl 1508.34007
Strange nonchaotic attractors in a quasiperiodically forced articulated mooring tower model. (English) Zbl 1498.37060
Modelling chaotic dynamical attractor with fractal-fractional differential operators. (English) Zbl 1525.34024
Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator. (English) Zbl 1498.34015
Self-similarity techniques for chaotic attractors with many scrolls using step series switching. (English) Zbl 1497.28004
Infinite number of parameter regions with fractal nonchaotic attractors in a piecewise map. (English) Zbl 1489.37045
Box dimension of fractal attractors and their numerical computation. (English) Zbl 1456.28006
Reviewer: George Stoica (Saint John)
Cantor set as a fractal and its application in detecting chaotic nature of piecewise linear maps. (English) Zbl 1512.28007
Mathematical analysis of memristor through fractal-fractional differential operators: a numerical study. (English) Zbl 1455.34048
Fractal dimension estimation with persistent homology: a comparative study. (English) Zbl 1451.62177
Wada fractal basins of attraction in a zero-stiffness vibration isolation system. (English) Zbl 1434.28044
Trinition the complex number with two imaginary parts: fractal, chaos and fractional calculus. (English) Zbl 1483.39008
Modeling attractors of chaotic dynamical systems with fractal-fractional operators. (English) Zbl 1448.65268
The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator. (Russian. English summary) Zbl 1463.37024
Exploring chaotic attractors in nonlinear dynamical system under fractal theory. (English) Zbl 1448.94005
Calculation the maximum Lyapunov exponent for the oscillatory system of Duffing with a degree memory. (Russian. English summary) Zbl 1408.34009
Fractal structures in the chaotic motion of charged particles in a magnetized plasma under the influence of drift waves. (English) Zbl 1400.78004
Chaotic behavior of modified stretch-twist-fold (STF) flow with fractal property. (English) Zbl 1390.37055
MSC:
37D45
37J45
Fractal dimension and Wada measure revisited: no straightforward relationships in NDDS. (English) Zbl 1375.28023
Evidence of chaos in EEG signals: an application to BCI. (English) Zbl 1359.92065
Azar, Ahmad Taher (ed.) et al., Advances in chaos theory and intelligent control. Cham: Springer (ISBN 978-3-319-30338-3/hbk; 978-3-319-30340-6/ebook). Studies in Fuzziness and Soft Computing 337, 609-625 (2016).
Discrete dynamics of one dimensional Collatz like integral value transformations. (English) Zbl 1358.37069
Dimensions of structurally stable and critical strange non-chaotic attractors. (English) Zbl 1351.37154
Orbit trap rendering methods for generating colorful symmetric images in three-dimensional space. (English) Zbl 1331.68255
A new encryption algorithm for color image based on a novel chaos with high fractal dimension. (Chinese. English summary) Zbl 1324.68242
New class of eighth-order iterative zero-finders and their basins of attraction. (English) Zbl 1301.41013
A method for calculating fractal dimension of multivariate time series. (Chinese. English summary) Zbl 1313.37041
Implications of the non-differentiability in the dynamics of discrete systems and field theory. Mathematical and physical aspects. I. (English) Zbl 1413.26010
Chaotic dynamical systems on fractals and their applications to image encryption. (English) Zbl 1350.94057
Li, Changpin (ed.) et al., Recent advances in applied nonlinear dynamics with numerical analysis. Fractional dynamics, network dynamics, classical dynamics and fractal dynamics with their numerical simulations. Festschrift dedicated to Zhong-hua Yang on the occasion of his 70th birthday. Hackensack, NJ: World Scientific (ISBN 978-981-4436-45-8/hbk; 978-981-4436-47-2/ebook). Interdisciplinary Mathematical Sciences 15, 279-304 (2013).
Study of the fractal solitons and chaotic behaviors for a \((2+1)\) -dimensional nonlinear partial differential equation. (English) Zbl 1254.35200
Chaos and fractals. An elementary introduction. (English) Zbl 1252.37001
Oxford: Oxford University Press (ISBN 978-0-19-956643-3/hbk; 978-0-19-956644-0/pbk). xxi, 408 p. (2012).
Reviewer: Thomas B. Ward (Durham)
Encounters with chaos and fractals. 2nd ed. (English) Zbl 1253.37001
Boca Raton, FL: CRC Press (ISBN 978-1-58488-517-7/hbk). xvi, 371 p. (2012).
Reviewer: Steve Pederson (Atlanta)
The chaos game revisited: Yet another, but a trivial proof of the algorithm’s correctness. (English) Zbl 1232.65178
Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)
Some open problems in the dynamics of quadratic and higher degree polynomial ODE systems. (English) Zbl 1271.34049
Zeraoulia, Elhadj (ed.) et al., Frontiers in the study of chaotic dynamical systems with open problems. Hackensack, NJ: World Scientific (ISBN 978-981-4340-69-4/hbk; 978-981-4340-70-0/ebook). World Scientific Series on Nonlinear Science. Series B: Special Theme Issues and Proceedings 16, 43-57 (2011).
Reviewer: Zaihong Wang (Beijing)
On a numerical aspect regarding the fractal dimension of a chaotic attractor. (Sur un aspect numérique de la dimension fractale d’un attracteur chaotique.) (English) Zbl 1265.37041
Global stability, limit cycles and chaotic behaviors of second order interpolative sigma delta modulators. (English) Zbl 1248.94036
Scale relativity and fractal space-time. A new approach to unifying relativity and quantum mechanics. (English) Zbl 1222.83004
London: Imperial College Press (ISBN 978-1-84816-650-9/hbk; 978-1-84816-651-6/ebook). xxi, 742 p. (2011).
Reviewer: Hans-Jürgen Schmidt (Potsdam)
Transient chaos. Complex dynamics in finite-time scales. (English) Zbl 1218.37005
Applied Mathematical Sciences 173. Berlin: Springer (ISBN 978-1-4419-6986-6/hbk; 978-1-4419-6987-3/ebook). xiv, 497 p. (2011).
Reviewer: Yuri V. Rogovchenko (Umeå)
Difference equations with continuous time: theory and applications. (English) Zbl 1217.39005
Elaydi, Saber (ed.) et al., Discrete dynamics and difference equations. Proceedings of the twelfth international conference on difference equations and applications (ICDEA), Lisbon, Portugal, July 23–27, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-4287-64-7/hbk). 104-119 (2010).
Asymptotic expansions for the escape rate of stochastically perturbed unimodal maps. (English) Zbl 1180.37036
A method of specification of fractal sets. (English. Russian original) Zbl 1189.28006
Cybern. Syst. Anal. 45, No. 3, 365-372 (2009); translation from Kibern. Sist. Anal. 2009, No. 3, 42-50 (2009).
Reviewer: Nicolae-Adrian Secelean (Sibiu)
Chaotic feature of Martin process imposed on the cosine function. (English) Zbl 1189.37037
Reviewer: Dieter Erle (Dortmund)
Noise-induced chaos: A consequence of long deterministic transients. (English) Zbl 1143.37312
MSC:
37D45
Bifurcations, chaos and synchronization in ADVP circuit with parallel resistor. (English) Zbl 1131.37037
Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems. (English) Zbl 1134.37365
Enhanced box and prism assisted algorithms for computing the correlation dimension. (English) Zbl 1131.65099
Likely limit sets of \(3\)-order nonsingle-valley Feigenbaum’s maps. (Chinese. English summary) Zbl 1140.39318
Newtonian dynamics in the plane corresponding to straight and cyclic motions on the hyperelliptic curve \(\mu^{2}= \nu^{n}-1, n \in \mathbb Z\): ergodicity, isochrony and fractals. (English) Zbl 1126.37040
Hausdorff dimension for some hyperbolic attractors with overlaps and without finite Markov partition. (English) Zbl 1131.37031
Reviewer: Bernd O. Stratmann (St. Andrews)
On the description of self-similarity for attractors by means of conditional entropy. (English) Zbl 1115.37033
High-dimensional chaotic and attractor systems. A comprehensive introduction. (English) Zbl 1118.37003
Reviewer: Boris V. Loginov (Ul’yanovsk)
Fractal sets from noninvertible maps. (English) Zbl 1162.28303
Novak, Miroslav M., Complexus mundi. Emergent patterns in nature. Hackensack, NJ: World Scientific (ISBN 981-256-666-X/hbk). 83-102 (2006).
Reviewer: Nicolae-Adrian Secelean (Sibiu)
A theory of fuzzy chaos for simulation and control of nonlinear systems. (English) Zbl 1125.37310
Li, Zhong (ed.) et al., Integration of fuzzy logic and chaos theory. Berlin: Springer (ISBN 978-3-540-26899-4/hbk). Studies in Fuzziness and Soft Computing 187, 391-414 (2006).
A novel chaotic dynamical system. (English) Zbl 1119.37029
MSC:
37D45
A new hyperchaotic system. (English) Zbl 1119.37028
MSC:
37D45
Fractal and chaotic patterns of general Korteweg-de Vries system in \((2+1)\)-dimensions. (English) Zbl 1127.35058
Analysis of surface EMG signals based on the change of phase space, entropy and complexity. (Chinese. English summary) Zbl 1105.37304
Superfractals. (English) Zbl 1123.28007
Cambridge: Cambridge University Press (ISBN 0-521-84493-2/hbk). xx, 453 p. (2006).
Reviewer: Uta Freiberg (Canberra)
Fractal Newton basins. (English) Zbl 1104.37034
On the Lyapunov dimension of the attractor of the Chirikov dissipative mapping. (English. Russian original) Zbl 1103.37014
Uraltseva, N.N.(ed.), Proceedings of the St. Petersburg Mathematical Society. Vol. X. Transl. from the Russian by Tamara Rozhkovskaya. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3861-X/hbk). Translations. Series 2. American Mathematical Society 214, 15-28 (2005); translation from Tr. St-Peterbg. Mat. Obshch. 10, 19-32 (2004).
Differential equations and dynamical systems, order and chaos. (Ecuaţii diferenţiale şi sisteme dinamice, ordine şi haos.) (Romanian) Zbl 1102.37022
Cluj-Napoca: U. T. Pres (ISBN 973-662-151-0/pbk). 159 p. (2005).
Reviewer: Emilia Petrisor (Timişoara)
On the role of chaotic saddles in generating chaotic dynamics in nonlinear driven oscillators. (English) Zbl 1089.37030
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