Global stability of local fractional Hénon-Lozi map using fixed point theory

Ibrahim, Rabha W.; Băleanu, Dumitru

doi:10.3934/math.2022636

Cited by 8 publications

(3 citation statements)

References 34 publications

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“…Ibrahim and Baleanu [40] used linear interpolation of quadratic and absolute value functions to define and study a combined Hénon-Lozi fractional map.…”

Section: Classic Fractional Lozi Mapmentioning

confidence: 99%

“…For all the attempted problems, DE and SOMA performed better than the Ziegler-Nichols method. In the ball and hoop system (40), DE and SOMA performed better than the Genetic Algorithm (GA), while in the electric DC motor problem (35) they obtained better overshoot and settling times compared to other heuristics (GA, PSO, Continuous Cycling [85], and Evolutionary Programming [86]). The authors found that DE and SOMA both achieved consistently better results.…”

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confidence: 99%

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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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“…Ibrahim and Baleanu [40] used linear interpolation of quadratic and absolute value functions to define and study a combined Hénon-Lozi fractional map.…”

Section: Classic Fractional Lozi Mapmentioning

confidence: 99%

mentioning

confidence: 99%

Survey of Recent Applications of the Chaotic Lozi Map

Lozi

2023

Algorithms

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“…A combined Hénon-Lozi fractional map was defined using a linear interpolation of quadratic and absolute value functions and studied by Ibrahim and Baleanu [46].…”

Section: Fractal Mappingsmentioning

confidence: 99%

Coexistence of Thread and Sheet Chaotic Attractors for Three-Dimensional Lozi Map

Lozi

2023

Dynamics

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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 or applied its properties in many fields (electronic devices such as memristors, A.I. with swarm intelligence, etc.). Several generalizations have been proposed, transforming the initial two-dimensional map into a multidimensional one. However, they do not respect the original constraint that allows this map to be one of the few strictly hyperbolic: a constant Jacobian. In this paper, we introduce a three-dimensional piece-wise linear extension respecting this constraint and we explore a special property never highlighted for chaotic mappings: the coexistence of thread chaotic attractors (i.e., attractors that are formed by a collection of lines) and sheet chaotic attractors (i.e., attractors that are formed by a collection of planes). This new three-dimensional mapping can generate a large variety of chaotic and hyperchaotic attractors. We give five examples of such behavior in this article. In the first three examples, there is the coexistence of thread and sheet chaotic attractors. However, their shapes are different and they are constituted by a different number of pieces. In the last two examples, the blow up of the attractors with respect to parameter a and b is highlighted.

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