Bifurcation and bursting oscillations in 2D non-autonomous discrete memristor-based hyperchaotic map

Deng, Yue; Li, Yuxia

doi:10.1016/j.chaos.2021.111064

Cited by 45 publications

(12 citation statements)

References 33 publications

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“…The intersection of saddle-node bifurcation and period-doubling bifurcation is labeled by LPPD, which is a codimension-2 bifurcation point. 12,12] in Fig. 3(b).…”

Section: Dynamical Regionmentioning

confidence: 98%

“…[3] Very recently, discrete memristor has begun to receive many researchers' attention. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] For instance, Peng et al presented a model of discrete memristor via the difference theory and derived a memristive Hénon map in Ref. [4].…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [12], Deng and Li established a class of 2D non-autonomous memristive maps that can display hyper-chaotic, periodic, and bursting oscillations. Deng and Li yielded a memristive sine map and studied non-parametric bifurcation and hyper-chaotic behaviors of the map in Ref.…”

Section: Introductionmentioning

confidence: 99%

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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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“…The intersection of saddle-node bifurcation and period-doubling bifurcation is labeled by LPPD, which is a codimension-2 bifurcation point. 12,12] in Fig. 3(b).…”

Section: Dynamical Regionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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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

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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 addition to the ideal DM model, a simple two-dimensional (2D) non-autonomous DMbased hyperchaotic map was proposed by Deng, which shows the bursting behaviors. [35] The above DM models and mappings all indicate that designing a chaotic discrete map with more complexities and better performances is still a valuable research topic.…”

Section: Introductionmentioning

confidence: 99%

Cascade discrete memristive maps for enhancing chaos*

Yuan¹,

Bai²,

Li³

2021

Chinese Phys. B

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Continuous-time memristor (CM) has been widely used to generate chaotic oscillations. However, discrete memristor (DM) has not been received adequate attention. Motivated by the cascade structure in electronic circuits, this paper introduces a method to cascade discrete memristive maps for generating chaos and hyperchaos. For a discrete-memristor seed map, it can be self-cascaded many times to get more parameters and complex structures, but with larger chaotic areas and Lyapunov exponents. Comparisons of dynamic characteristics between the seed map and cascading maps are explored. Meanwhile, numerical simulation results are verified by the hardware implementation.

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Bifurcation and bursting oscillations in 2D non-autonomous discrete memristor-based hyperchaotic map

Cited by 45 publications

References 33 publications

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

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

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

Cascade discrete memristive maps for enhancing chaos*

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