Abstract:
The dynamics of two coupled antiphase driven Toda oscillators is studied. We demonstrate three different routes of transition to chaotic dynamics associated with different bifurcations of periodic and quasi-periodic regimes. As a result of these, two types of chaotic dynamics with one and two positive Lyapunov exponents are observed. We argue that the results obtained are robust as they can exist in a wide range of the system parameters.
N.V.S. acknowledges partial support from the grant of the President of the Russian Federation (MK-661.2017.8), V.V.A. thanks for partial financial support from the Russian Ministry of Science and Education (Project 9.2108.2017/4.6).
Citation:
Nataliya V. Stankevich, Anton Dvorak, Vladimir Astakhov, Patrycja Jaros, Marcin Kapitaniak, Przemyslaw Perlikowski, Tomasz Kapitaniak, “Chaos and Hyperchaos in Coupled Antiphase Driven Toda Oscillators”, Regul. Chaotic Dyn., 23:1 (2018), 120–126
\Bibitem{StaDvoAst18}
\by Nataliya V. Stankevich, Anton Dvorak, Vladimir Astakhov, Patrycja Jaros, Marcin Kapitaniak, Przemyslaw Perlikowski, Tomasz Kapitaniak
\paper Chaos and Hyperchaos in Coupled Antiphase Driven Toda Oscillators
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 1
\pages 120--126
\mathnet{http://mi.mathnet.ru/rcd312}
\crossref{https://doi.org/10.1134/S1560354718010094}
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This publication is cited in the following 30 articles:
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A. Kilina, P. Panteleeva, N. Stankevich, “Multi-dimensional chaos initiated by short pulses in non-autonomous radio-physical generator”, Communications in Nonlinear Science and Numerical Simulation, 2024, 108041
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Nataliya Stankevich, “Stabilization and complex dynamics initiated by pulsed force in the Rössler system near saddle-node bifurcation”, Nonlinear Dyn, 112:4 (2024), 2949
Yang Cao, Peiyu Guo, Luca Guerrini, “Hopf Bifurcation of the Ring Unidirectionally Coupled Toda Oscillators with Distributed Delay”, Int. J. Bifurcation Chaos, 34:12 (2024)
S. Leo Kingston, Marek Balcerzak, Syamal K. Dana, Tomasz Kapitaniak, “Transition to hyperchaos and rare large-intensity pulses in Zeeman laser”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 33:2 (2023)
Jinbin Wang, Rui Zhang, Jiankang Liu, “Vibrational resonance analysis in a fractional order Toda oscillator model with asymmetric potential”, International Journal of Non-Linear Mechanics, 148 (2023), 104258
Xiu Zhao, Xingyuan Wang, Yining Su, Salahuddin Unar, “Network dynamics of a periodically forced chemical system and its application for tuning PID controller with time-delay systems”, Nonlinear Dyn, 111:14 (2023), 13601
Nataliya Stankevich, Evgeny Volkov, “Emergence and evolution of unusual inhomogeneous limit cycles displacing hyperchaos in three quorum-sensing coupled identical ring oscillators”, Physica D: Nonlinear Phenomena, 455 (2023), 133902
Jie Zhang, Jinyou Hou, Longhao Xu, Xiaopeng Zhu, Qinggang Xie, “Dynamical analysis, circuit implementation, and simultaneous application of a novel four-dimensional hyperchaotic system based on cosine functions”, Microelectronic Engineering, 271-272 (2023), 111939
Péter Krähling, Joshua Steyer, Ulrich Parlitz, Ferenc Hegedűs, “Attractor selection in nonlinear oscillators by temporary dual-frequency driving”, Nonlinear Dyn, 111:20 (2023), 19209
S. Leo Kingston, Tomasz Kapitaniak, Syamal K. Dana, “Transition to hyperchaos: Sudden expansion of attractor and intermittent large-amplitude events in dynamical systems”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 32:8 (2022)
I. R. Garashchuk, “Asynchronous Chaos and Bifurcations in a Model of
Two Coupled Identical Hindmarsh – Rose Neurons”, Rus. J. Nonlin. Dyn., 17:3 (2021), 307–320
N. Stankevich, E. Volkov, “Chaos-hyperchaos transition in three identical quorum-sensing mean-field coupled ring oscillators”, Chaos, 31:10 (2021), 103112
O. Kolebaje, O. O. Popoola, U. E. Vincent, “Occurrence of vibrational resonance in an oscillator with an asymmetric Toda potential”, Physica D, 419 (2021), 132853
I. R. Garashchuk, D. I. Sinelshchikov, “Bubbling transition as a mechanism of destruction of synchronous oscillations of identical microbubble contrast agents”, Chaos, 31:2 (2021), 023130
I. R. Sataev, N. V. Stankevich, “Cascade of torus birth bifurcations and inverse cascade of Shilnikov attractors merging at the threshold of hyperchaos”, Chaos, 31:2 (2021), 023140
B. P. Bezruchko, V. I. Ponomarenko, Y. P. Seleznev, “Experimental Studies of Chaotic Dynamics Near the Theorist”, Izv. Vyss. Uchebn. Zaved.-Prikl. Nelineynaya Din., 29:1 (2021), 88–135
R. Su, Ch. Zhang, “Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay”, Nonlinear Anal.-Model Control, 26:3 (2021), 375–395
N. Stankevich, A. Kazakov, S. Gonchenko, “Scenarios of hyperchaos occurrence in 4D rossler system”, Chaos, 30:12 (2020), 123129
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