Multistability and Four-Scroll Chaos in a Pair of Coupled Second-Order Damped Oscillators with Hyperbolic Sine Function: Theoretical Study and Circuit Simulation

Sriram, Sridevi; Kana Kemgang, Lucas; Rakhmatullaeva, M. F.; Rajagopal, Karthikeyan; Kengne, Jacques

doi:10.1007/s00034-023-02573-2

Circuits Syst Signal Process

2023

DOI: 10.1007/s00034-023-02573-2

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Multistability and Four-Scroll Chaos in a Pair of Coupled Second-Order Damped Oscillators with Hyperbolic Sine Function: Theoretical Study and Circuit Simulation

Sridevi Sriram,

Lucas Kana Kemgang,

M. F. Rakhmatullaeva

et al.

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2024

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Cited by 2 publications

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Design and application of multiscroll chaotic attractors based on memristors

Zhang,

Wei,

Zuo

et al. 2024

Integration

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Design and application of multiscroll chaotic attractors based on memristors

Zhang,

Wei,

Zuo

et al. 2024

Integration

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Most probable trajectories of a birhythmic oscillator under random perturbations

Zhang,

Xu,

Tang

et al. 2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This study investigates the most probable trajectories of a birhythmic oscillator under stochastic perturbations. The distinctive feature of the birhythmic oscillator is the coexistence of two stable limit cycles with different amplitudes and frequencies, separated by an unstable limit cycle. The path integral method was utilized to compute the instantaneous probability density. Based on the theory of most probable dynamics, by maximizing the probability density function, we present the time series of the most probable trajectories starting from different initial states. Furthermore, we conducted a detailed analysis of the noise-induced transitions between the two stable limit cycles under different parameter conditions. This approach enables us to understand and track the most probable escape time and specific most probable trajectories as the system transitions from the basin of attraction of one stable limit cycle to another. This work visualizes the most probable trajectories in stochastic systems and provides an innovative solution to the complex problem of noise-induced transitions between two stable limit cycles. Our research aims to provide a new perspective for studying complex stochastic dynamical systems.

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Multistability and Four-Scroll Chaos in a Pair of Coupled Second-Order Damped Oscillators with Hyperbolic Sine Function: Theoretical Study and Circuit Simulation

Cited by 2 publications

References 50 publications

Design and application of multiscroll chaotic attractors based on memristors

Design and application of multiscroll chaotic attractors based on memristors

Most probable trajectories of a birhythmic oscillator under random perturbations

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