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

Zhang, Liping; Liu, Yang; Wei, Zhouchao; Jiang, Haibo; Lyu, Wei-Peng; Bi, Qinsheng

doi:10.1088/1674-1056/ac7294

Cited by 14 publications

(12 citation statements)

References 45 publications

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“…Many researchers have devoted themselves to the analysis of chaotic phenomena in discrete memristors. Recently, hidden attractors have been discovered in discrete memristor-based maps [50]. Wang et al [51] included a discrete-time memristor to create a memristive Lozi map.…”

Section: Memristor-based Lozi Map With Hidden Hyperchaosmentioning

confidence: 99%

Survey of Recent Applications of the Chaotic Lozi Map

Lozi

2023

Algorithms

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Since its original publication in 1978, Lozi’s chaotic map has been thoroughly explored and continues to be. Hundreds of publications have analyzed its particular structure and applied its properties in many fields (e.g., improvement of physical devices, electrical components such as memristors, cryptography, optimization, evolutionary algorithms, synchronization, control, secure communications, AI with swarm intelligence, chimeras, solitary states, etc.) through algorithms such as the COLM algorithm (Chaotic Optimization algorithm based on Lozi Map), Particle Swarm Optimization (PSO), and Differential Evolution (DE). In this article, we present a survey based on dozens of articles on the use of this map in algorithms aimed at real applications or applications exploring new directions of dynamical systems such as chimeras and solitary states.

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Section: Memristor-based Lozi Map With Hidden Hyperchaosmentioning

confidence: 99%

Survey of Recent Applications of the Chaotic Lozi Map

Lozi

2023

Algorithms

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“…In [39], Peng et al analyzed the behavior of the higher-dimensional discrete memristor map, whereas a new discrete memristor chaotic map has been constructed in [36]. The hyperchaotic of the 2D symmetric map with complete control is demonstrated in [37], while the hidden multistability of the 2D maps with a cosine memristor has been studied in [38]. The majority of the aforementioned discrete memristor research is of classical integer order, but unfortunately, the discrete fractional memristor study is inadequate as there are relatively few studies on it.…”

Section: Introductionmentioning

confidence: 99%

Hidden multistability of fractional discrete non-equilibrium point memristor based map

et al. 2023

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At present, the multistability analysis in discrete nonlinear fractional-order systems is a subject that is receiving a lot of attention. In this article, a new discrete non-equilibrium point memristor-based map with $\gamma-th$ Caputo fractional difference is introduced. In addition, in the context of the commensurate and non-commensurate instances, the non-linear dynamics of the suggested discrete fractional map, such as its multistability, hidden chaotic attractor, and hidden hyperchaotic attractor, are investigated through several numerical techniques, including Lyapunov exponents, phase attractors, bifurcation diagrams, and the $0–1$ test. This dynamic behaviors suggests that the fractional discrete memristive map has a hidden multistability. Finally, to validate the presence of chaos, a complexity analysis is carried out using approximation entropy ($ApEn$) and the $C_0$ measure. The findings show that the model has a high degree of complexity, which is affected by the system parameters and the fractional values.

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“…Considering different purposes, there is also other research on chaotic maps. For instance, a hyperchaotic map based on offset boosting [20], a memristive map with a cosine memristor and hidden multistable dynamics [21], and 2D rational memristive maps with hidden attractors and various solutions [22]. Additionally, a comprehensive fine-scale analysis of the dynamical response across wide parameter ranges of the 2D Rulkov map was presented in [23].…”

Section: Introductionmentioning

confidence: 99%

A novel chaotic map with a shifting parameter and stair-like bifurcation diagram: dynamical analysis and multistability

Ramadoss¹,

Natiq²,

Nazarimehr

et al. 2023

Phys. Scr.

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In this paper, the behavior of a 1D chaotic map is proposed which includes two sine terms and shows unique dynamics. By varying the bifurcation parameter, the map has a shift, and the system's dynamics are generated around the cross points of the map and the identity line. The irrational frequency of the sine term makes the system have stable fixed points in some parameter intervals by increasing the bifurcation parameter. So, the bifurcation diagram of the system shows that the trend of the system's dynamics changes in a stair shape with slope one by changing the bifurcation parameter. Due to the achieving multiple steady states in some intervals of the parameter, the proposed system is known as multistable. The multistability dynamics of the map are investigated with the help of cobweb diagrams which reveal an interesting asymmetry in repeating parts of the bifurcation diagram.

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

Cited by 14 publications

References 45 publications

Survey of Recent Applications of the Chaotic Lozi Map

Survey of Recent Applications of the Chaotic Lozi Map

Hidden multistability of fractional discrete non-equilibrium point memristor based map

A novel chaotic map with a shifting parameter and stair-like bifurcation diagram: dynamical analysis and multistability

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