Various coexisting attractors, asymmetry analysis and multistability control in a 3D memristive jerk system

Kengne, Léandre Kamdjeu; Muni, Sishu Shankar; Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere

doi:10.1140/epjp/s13360-022-03073-z

Cited by 16 publications

(6 citation statements)

References 28 publications

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“…Under the effect of some physical parameters such as the non-linearity coefficient and the coupled magnetic flux, the domain where the influence of a parameter can be exerted can appear or disappear as a function of a chosen variable [43]. This is the case of the Van der Pol (VdP) biological model, van der Pol-Duffing [43,44], the hyperjeck system [44], memristive Jerk system [45] and many others. The antimonotonicity in the model is characterized by a periodic zone on either side and separated by irregular, chaotic envelopes that remain symmetrical for the chosen conditions [46]; figure 15…”

Section: Reemerging Feigenbaum and Anti-monotonicitymentioning

confidence: 99%

Influence of the magnetic flux on the dynamics of a self-sustaining system: analytical, numerical and analogical investigations

Dang-Ra,

Chéagé Chamgoué,

Wouapi

et al. 2024

Phys. Scr.

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This paper investigates the nonlinear dynamics of a ferroelectric enzyme-substratereaction modeled by \textcolor{red}{the} bi-rhythmic \emph{van der Pol} oscillator coupled to \textcolor{red}{the} magneticflux. We derive the equilibrium points and study their stability.We analyze some bifurcation structures and the variation of the Lyapunov exponents.The phenomena of symmetric attractors and the anti-monotonicity are observed. \textcolor{red}{By} increasing the magnetic flux, \textcolor{red}{we find that the equilibrium points are stable}, tends to control chaotic regimes, and affects regular and quasi-regular ones. As the magnetic flux increases, the amplitude of the oscillations around the equilibrium points decreases and the \textcolor{red}{amplitude of the} limit cycles at the Hopf bifurcation \textcolor{red}{tends} to disappear. Further \textcolor{red}{increasing the magnetic flux gives} rise to chaotic dynamics. The electrical circuit and analogical simulations are \textcolor{red}{derived} using the PSpice software.\textcolor{red}{The agreement between analogical and numerical results is acceptable}.

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Section: Reemerging Feigenbaum and Anti-monotonicitymentioning

confidence: 99%

Influence of the magnetic flux on the dynamics of a self-sustaining system: analytical, numerical and analogical investigations

Dang-Ra,

Chéagé Chamgoué,

Wouapi

et al. 2024

Phys. Scr.

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“…[43][44][45][46][47][48][49][50][51] As a result, research on discrete neurons has become a hot topic in recent years. In discrete memristor-coupled neural networks, complex dynamical behaviors have been discovered, including coexisting attractors, [52][53][54][55][56] synchronization transitions, and synchronization coexistence. [57,58] Additionally, Lu et al [59] investigated fractional-order neural networks based on discrete memristors and found that this system exhibits richer dynamical behaviors compared to integer-order neural networks.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Ma 马,

Xiong 熊,

Li 李

et al. 2024

Chinese Phys. B

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Synaptic crosstalk is a prevalent phenomenon among neuronal synapses, playing a crucial role in the transmission of neural signals. Therefore, considering synaptic crosstalk behavior and investigating the dynamical behavior of discrete neural networks is highly necessary. In this paper, we propose a heterogeneous discrete neural network (HDNN) consisting of a three-dimensional KTz discrete neuron and a Chialvo discrete neuron. These two neurons are coupled mutually by two discrete memristors and the synaptic crosstalk is considered. The impact of crosstalk strength on the firing behavior of the HDNN is explored through bifurcation diagrams and Lyapunov exponents. It is observed that the HDNN exhibits different coexisting attractors under varying crosstalk strengths. Furthermore, the influence of different crosstalk strengths on the synchronized firing of the HDNN is investigated, revealing a gradual attainment of phase synchronization between the two discrete neurons as the crosstalk strength decreases.

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“…Rajagopal et al [14] proposed a new dissipative chaotic jerk system with two quadratic nonlinearities, discussed its dynamic properties, and provided a circuit realization of the new jerk system. Chaotic jerk systems have applications in many areas, such as oscillators [3,15], microcontrollers [16], circuits [17,18], memristors [19,20], encryption [21], etc.…”

Section: Introductionmentioning

confidence: 99%

FPGA-Based Implementation of a New 3-D Multistable Chaotic Jerk System with Two Unstable Balance Points

et al. 2023

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Mechanical jerk systems have applications in several areas, such as oscillators, microcontrollers, circuits, memristors, encryption, etc. This research manuscript reports a new 3-D chaotic jerk system with two unstable balance points. It is shown that the proposed mechanical jerk system exhibits multistability with coexisting chaotic attractors for the same set of system constants but for different initial states. A bifurcation analysis of the proposed mechanical jerk system is presented to highlight the special properties of the system with respect to the variation of system constants. A field-programmable gate array (FPGA) implementation of the proposed mechanical jerk system is given by synthesizing the discrete equations that are obtained by applying one-step numerical methods. The hardware resources are reduced by performing pipeline operations, and, finally, the paper concludes that the experimental results of the proposed mechanical jerk system using FPGA-based design show good agreement with the MATLAB simulations of the same system.

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Various coexisting attractors, asymmetry analysis and multistability control in a 3D memristive jerk system

Cited by 16 publications

References 28 publications

Influence of the magnetic flux on the dynamics of a self-sustaining system: analytical, numerical and analogical investigations

Influence of the magnetic flux on the dynamics of a self-sustaining system: analytical, numerical and analogical investigations

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

FPGA-Based Implementation of a New 3-D Multistable Chaotic Jerk System with Two Unstable Balance Points

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