Memristive Hénon map with hidden Neimark–Sacker bifurcations

Rong, Kang; Bao, Han; Li, Houzhen; Hua, Zhongyun; Bao, Bocheng

doi:10.1007/s11071-022-07380-z

Cited by 36 publications

(10 citation statements)

References 36 publications

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“…Theorem 1 states that ( 14) has an asymptotically stable zero equilibrium. This implies that the chaotic trajectories of this proposed FODTS (3) are stabilized by the linear control law (13).…”

Section: Control Lawsmentioning

confidence: 88%

“…The dynamic behavior of a higher-dimensional fractional-order chaotic map was described by Peng et al in [11] that same year, while Wang et al examined the chaos and complexity of a fractional order higher-dimensional multi-cavity chaotic map in [12]. Memristive maps with integer and fractional orders have recently been proposed [13,14]. A memristor-based Rulkov neuron map was introduced in [15] by using a discrete memristor to replicate the magnetic effects, whereas [16] illustrated the dynamic features of a novel discrete memristive hyperchaotic map.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hidden Homogeneous Extreme Multistability of a Fractional-Order Hyperchaotic Discrete-Time System: Chaos, Initial Offset Boosting, Amplitude Control, Control, and Synchronization

et al. 2023

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Fractional order maps are a hot research topic; many new mathematical models are suitable for developing new applications in different areas of science and engineering. In this paper, a new class of a 2D fractional hyperchaotic map is introduced using the Caputo-like difference operator. The hyperchaotic map has no equilibrium and lines of equilibrium points, depending on the values of the system parameters. All of the chaotic attractors generated by the proposed fractional map are hidden. The system dynamics are analyzed via bifurcation diagrams, Lyapunov exponents, and phase portraits for different values of the fractional order. The results show that the fractional map has rich dynamical behavior, including hidden homogeneous multistability and offset boosting. The paper also illustrates a novel theorem, which assures that two hyperchaotic fractional discrete systems achieve synchronized dynamics using very simple linear control laws. Finally, the chaotic dynamics of the proposed system are stabilized at the origin via a suitable controller.

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Section: Control Lawsmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Hidden Homogeneous Extreme Multistability of a Fractional-Order Hyperchaotic Discrete-Time System: Chaos, Initial Offset Boosting, Amplitude Control, Control, and Synchronization

et al. 2023

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“…Recently, many memristor-based discrete maps have successively been proposed by introducing some discrete memristor models into the existing discrete maps [37][38][39][40][41][42][43]. Motivated by the above analysis, this paper constructs a novel memristor-based neuron model by coupling a discrete memristor with an existing map-based neuron model [24].…”

Section: Introductionmentioning

confidence: 99%

Memristor-induced mode transitions and extreme multistability in a map-based neuron model

Bao

Cai

et al. 2022

Nonlinear Dyn

Self Cite

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Because of the advent of discrete memristor, memristor effect in discrete map has become the important subject deserving discussion. To this end, this paper constructs a memristor-based neuron model considering magnetic induction by combining an existing map-based neuron model and a discrete memristor with absolute value nonlinear memductance. Taking the coupling strength and initial state of the memristor as variables, complex mode transition behaviors induced by the introduced memristor are disclosed using numerical methods, including spiking-bursting behaviors, mode transition behaviors, and hyperchaotic spiking behaviors. In particular, all of these behaviors are greatly dependent on the memristor initial state, resulting in the existence of extreme multistability in the memristive neuron model.Therefore, this memristive neuron model can be used to effectively imitate the magnetic induction effects when complex mode transition behaviors appear in the neuronal action potential. Besides, an FPGAbased hardware platform is developed for implementing the memristive neuron model and various spiking-bursting sequences are experimentally captured therein. The results show that when biophysical memory effect is present, the memristive neuron model can better represent the ring activities of biological neurons than the original map-based neuron model.

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“…In Ref. [22], Rong et al constructed a 3D memristive map by coupling a discrete tangent memristor to the Hénon map. Peng et al gave three 2D memristive sine maps by introducing three discrete memristor models into the sine map in Ref.…”

Section: Introductionmentioning

confidence: 99%

Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor

et al. 2022

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In this work, we present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are demonstrated and investigated using different numerical tools, including phase portrait, basins of attraction, bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map has been carried out to reveal the bifurcation mechanism of the dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors. They can exhibit extremely hidden multi-stability, namely the coexistence of infinite hidden attractors, rarely shown in memristive maps. Potentially, this work can be used for secure communication, such as data and image encryption.

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Memristive Hénon map with hidden Neimark–Sacker bifurcations

Cited by 36 publications

References 36 publications

Hidden Homogeneous Extreme Multistability of a Fractional-Order Hyperchaotic Discrete-Time System: Chaos, Initial Offset Boosting, Amplitude Control, Control, and Synchronization

Hidden Homogeneous Extreme Multistability of a Fractional-Order Hyperchaotic Discrete-Time System: Chaos, Initial Offset Boosting, Amplitude Control, Control, and Synchronization

Memristor-induced mode transitions and extreme multistability in a map-based neuron model

Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor

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