A Novel Memristor-Based Dynamical System with Chaotic Attractor and Periodic Bursting

Yan, Shaohui; Song, Zhenlong; Shi, Wanlin; Zhao, Weilong; Ren, Yan; Sun, Xiaodan

doi:10.1142/s021812742250047x

Cited by 8 publications

(5 citation statements)

References 34 publications

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“…When A is fixed at 4 V, and F is set at 1 Hz, 2 Hz, and 5 Hz, respectively, the pinched hysteresis loops of W1 and W 2 are shown in figures 1(a) and (c), when F = 2 Hz is maintained and A is determined as 2 V, 3 V, and 4 V, respectively, the pinched hysteresis loop of W1 and W 2 are shown in figures 1(b) and (d). Obviously, the numerical results indicate that the hysteresis loop pinched at the origin and its area decreases with increasing the frequency or reducing the amplitude [62].…”

Section: A 4d Hr Neuron Model Based On Two Memristors 21 Memristor Mo...mentioning

confidence: 91%

Four-dimensional Hindmarsh–Rose neuron model with hidden firing multistability based on two memristors

Yan¹,

Zhang²,

Yu³

et al. 2022

Phys. Scr.

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Since memristors can be used to describe electromagnetic induction effects, this paper proposes a novel 4-D Hindmarsh-Rose (HR) neuron model based on two flux-controlled memristors to show complex dynamics of neuronal electrical activity. It has no equilibrium point, revealing hidden dynamical behaviors. The complex dynamics of the system are illustrated by phase portraits, the time sequences, bifurcation diagrams, and Lyapunov exponents spectra. The presented 4-D HR neuron model can produce coexisting multiple hidden firing patterns, for instance, periodic spiking, chaotic spiking, transient chaotic spiking, periodic bursting, chaotic bursting, transient chaotic bursting, stochastic bursting, and transient stochastic bursting. Besides, rich nonlinear dynamics, such as anti-monotonicity and initial offset boosting, are also found. Finally, Multisim circuit simulation is performed and the results are in accordance with numerical simulation.

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Section: A 4d Hr Neuron Model Based On Two Memristors 21 Memristor Mo...mentioning

confidence: 91%

Four-dimensional Hindmarsh–Rose neuron model with hidden firing multistability based on two memristors

Yan¹,

Zhang²,

Yu³

et al. 2022

Phys. Scr.

Self Cite

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“…The switched system circuit built based on Multisim is shown in figure 23, and the corresponding circuit equation can be written according to the circuit schematic as equation (20). = -…”

Section: Circuit Simulation and Dsp Implementationmentioning

confidence: 99%

“…Han Bao et al proposed a new 5-D twomemristor-based jerk system and studied complex dynamical effects induced by memristor and non-memristor initial conditions therein [19]. Shaohui Yan et al proposed a generalized memristor, constructing a simple ternary chaotic oscillator according to Chua's theory,confirming chaotic bursting and periodic bursting phenomena of the system [20]. Numerous studies have shown that chaotic systems composed of memristors usually exhibit complex nonlinear dynamic characteristics.…”

Section: Introductionmentioning

confidence: 99%

Complex dynamics analysis and feedback control for a memristive switched chaotic system

Shi,

Du,

Liu

2023

Phys. Scr.

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A switched chaotic system is proposed by connecting the memristor to the Rössler system through a time-switching function in this paper. Under the action of the switching function, the system can achieve switching between two subsystems with different structures. The switched system has super multiple coexisting attractors for different initial values, there are chaotic and quasi-periodic offset boosting, as well as various transient transition behaviors. It is interesting to note that besides the initial-dependent offset boosting, there are three other types of offset boosting behaviors, of which time-based offset boosting has not been found in other systems. In addition, the switching function can make the attractor self-replicate and produce intermittent chaos, and transient transition behavior also occurs in a short time during the intermittent process. These findings indicate that the switched system has complex dynamic characteristics. Both analog and DSP digital circuits confirm the physical feasibility of the novel offset-boosting behavior. Finally, to further implement the switched system in engineering applications, we designed a feedback controller. Matlab numerical calculations and Multisim circuit simulation demonstrate that the state variables of each subsystem can be well controlled under the action of the feedback controller.

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“…In recent years, there has been a significant surge in numerous disciplines dedicated to the examination of the classical Lorenz system [3], generalized Lorenz systems [4] and Lorenz-like systems [5]. These systems include the Chen system [6], the Schr ödinger system [7], the memristor-based dynamical system [8] and others.…”

Section: Introductionmentioning

confidence: 99%

Jacobi Stability Analysis of Liu System: Detecting Chaos

Liu,

Zhang

2024

Mathematics

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By utilizing the Kosambi–Cartan–Chern (KCC) geometric theory, this paper is dedicated to providing novel insights into the Liu dynamical system, which stands out as one of the most distinctive and noteworthy nonlinear dynamical systems. Firstly, five important geometrical invariants of the system are obtained by associating the nonlinear connection with the Berwald connection. Secondly, in terms of the eigenvalues of the deviation curvature tensor, the Jacobi stability of the Liu dynamical system at fixed points is investigated, which indicates that three fixed points are Jacobi unstable. The Jacobi stability of the system is analyzed and compared with that of Lyapunov stability. Lastly, the dynamical behavior of components of the deviation vector is studied, which serves to geometrically delineate the chaotic behavior of the system near the origin. The onset of chaos for the Liu dynamical system is obtained. This work provides an analysis of the Jacobi stability of the Liu dynamical system, serving as a useful reference for future chaotic system research.

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A Novel Memristor-Based Dynamical System with Chaotic Attractor and Periodic Bursting

Cited by 8 publications

References 34 publications

Four-dimensional Hindmarsh–Rose neuron model with hidden firing multistability based on two memristors

Four-dimensional Hindmarsh–Rose neuron model with hidden firing multistability based on two memristors

Complex dynamics analysis and feedback control for a memristive switched chaotic system

Jacobi Stability Analysis of Liu System: Detecting Chaos

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