Effect of amplitude-modulated force on horseshoe dynamics in Briggs–Rauscher chemical system modeled by a new parametric oscillator with asymmetric potential

Kpomahou, Y. J. F.; Adomou, A.; Yamadjako, A. E.; Djossou, Julien

doi:10.1140/epjp/s13360-022-02903-4

Cited by 7 publications

(4 citation statements)

References 25 publications

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“…In this section of the paper, the dynamical behavior of the novel, extremely complex two-scroll hyperchaotic system (1) is examined with Z(0) � (0.8, 0.2, 0.4, 0.6). [5,25]. e outcomes of the simulation show that, depending on the value of parameter a, system (1) can display a variety of types of behavior such as periodic, chaotic, or hyperchaotic behavior with varying degrees of complexity.…”

Section: A Bifurcation Study Of the Hyperchaotic Two-scroll Attractormentioning

confidence: 99%

“…Due to the rapid advancement of chaos theory, chaotic and hyperchaotic systems are applicable in several engineering branches such as memristive circuits [1][2][3][4], chemical oscillators [5][6][7], information sensing systems [8][9][10], lasers [11,12], and communication systems [13][14][15][16]. Xiu et al [17] designed a 5-D hyperchaotic system with hardware circuit design developed from a memristive cellular neural network (CNN) and applied it to build a secure communication system.…”

Section: Introductionmentioning

confidence: 99%

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A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

Vaidyanathan

Sambas

Tlelo‐Cuautle

et al. 2022

Discrete Dynamics in Nature and Society

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With the swift advancement of chaos theory, the modeling, chaotic oscillations, and engineering applications of chaotic and hyperchaotic systems are important topics in research. In this research paper, we elucidate our findings of a new four-dimensional two-scroll hyperchaotic system having only two quadratic nonlinearities and carry out a detailed bifurcation study of the proposed dynamical model. Also, an electronic circuit has been constructed for the new system using MultiSim (Version 14). The implementation of the new 4-D hyperchaotic system in a field-programmable gate array (FPGA) is performed herein by applying two numerical methods, viz. Forward Euler Method and Trapezoidal Method. The experimental results show a good match with the simulated hyperchaotic attractors. We also provide details of the hardware resources used for an FPGA Basys 3 Xilinx Artix-7 XC7A35T-ICPG236C.

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Section: A Bifurcation Study Of the Hyperchaotic Two-scroll Attractormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

Vaidyanathan

Sambas

Tlelo‐Cuautle

et al. 2022

Discrete Dynamics in Nature and Society

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“…In control theory, it's employed to examine resonant phenomena and control signals in systems [30,31]. Moreover, amplitude modulation is also applied in studying chaotic phenomena and fractal structures in modulation [32,33]. By simulating the amplitude modulation processes in these systems, researchers can reveal key features of system dynamics, such as stability, chaotic behavior, and frequency response characteristics [34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Amplitude modulation leads to the disappearance of relaxation oscillations in the Duffing system

Song,

Jiang,

Han

et al. 2024

Phys. Scr.

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Relaxation oscillations are pervasive in diverse areas of natural sciences and engineering, and exploring the dynamical mechanisms of relaxation oscillations is one of the most significant issues. Typical relaxation oscillations can be observed in the Duffing system. Recently, amplitude modulation has emerged as a novel control mechanism for investigating the behavior of fast-slow dynamics in systemic tension oscillations. It has demonstrated the ability to prolong the quasi-static slow process of the system and increase the number of bifurcation points. However, the exploration of the mechanistic aspects of amplitude modulation is still in its early stages, with many unreported dynamical mechanisms. Among these, investigating the modes of relaxation oscillations induced by amplitude modulation is one of the most important issues. Therefore, this manuscript focuses on studying the effect of amplitude modulation on relaxation oscillations, using the classical forced Duffing system as a representative model. Significantly, we report an intriguing finding for the first time, revealing a new amplitude-modulated mechanism by which the disappearance of relaxation oscillations can be induced. By employing the fast-slow analysis, we have examined the underlying dynamical mechanisms, revealing a strong correlation with the modulation index of amplitude modulation. Notably, when the system operates under low amplitude modulation, an extension of the quasi-static process is observed, manifesting as a prolonged slow process. Conversely, under high amplitude modulation, relaxation oscillations suddenly disappear. Our results serve to enrich the potential mechanisms of amplitude modulation, and our analysis provides a reference for investigating the dynamical behavior induced by amplitude modulation in other dynamical systems.

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“…In this perspective, bursting and mixed-mode oscillations, coexisting attractors and homoclinic bifurcation have been investigated in a mixed Rayleigh-Liénard oscillator under periodic parametric damping and external excitations [25,26]. Recently, regular, chaotic behaviors and coexisting attractors have been investigated in a new nonlinear dissipative chemical oscillator subjected to periodic parametric damping and external excitations [27,28]. The effect of linear periodic parametric damping in the study of chaos control of a Bonhoeffen-Van der pol oscillator has been studied numerically [29].…”

Section: Introductionmentioning

confidence: 99%

Effects of periodic parametric damping and amplitude-modulated signal on vibrational resonance and torus-doubling bifurcations occurrence in an asymmetric mixed Rayleigh-Liénard oscillator

Adéyémi,

Kpomahou,

Agbélélé

et al. 2023

Phys. Scr.

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This research paper examines the effects of periodic parametric damping and amplitude-modulated signal on vibrational resonance and the occurrence of torus-doubling bifurcations in an asymmetric mixed Rayleigh-Liénard oscillator. The method of direct separation of the slow and fast motions is used to derive the approximate theoretical expression of response amplitude at the low frequency. The obtained results show that the presence of periodic parametric damping induces in the system multiple resonance peaks when the low frequency is varied. Moreover, the increase of carrier amplitude modulated increases or decreases the maximum amplitude value in certain range of the low frequency. However, when the periodic parametric damping coefficient is varied, one resonance peaks occurs and the maximum amplitude value increases when the carrier amplitude modulated increases. The theoretical and direct numerical predictions have shown a fairly satisfactory agreement. On the other hand, the global dynamical changes of the system are numerically examined in context of vibrational resonance. It is found that, the system displays many torus attractors of different topologies, torus-doubling bifurcations, reverse torus-doubling bifurcations and torus-chaos. These observations are illustrated by plotting the phase portraits and their corresponding Poincaré maps.

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Effect of amplitude-modulated force on horseshoe dynamics in Briggs–Rauscher chemical system modeled by a new parametric oscillator with asymmetric potential

Cited by 7 publications

References 25 publications

A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

Amplitude modulation leads to the disappearance of relaxation oscillations in the Duffing system

Effects of periodic parametric damping and amplitude-modulated signal on vibrational resonance and torus-doubling bifurcations occurrence in an asymmetric mixed Rayleigh-Liénard oscillator

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