Li–Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice

Khellat, Farhad; Ghaderi, Akashe; Vasegh, Nastaran

doi:10.1016/j.chaos.2011.07.015

Cited by 48 publications

(7 citation statements)

References 12 publications

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“…It has been found that chaos is useful under some circumstances, such as in human-brain analysis [2], heartbeat regulation [3], and digital communications [4]. Now, it has attracted increasing attention partially due to its great potential in many nontraditional applications [5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…The Couple Map Lattice (CML) is a classical spatiotemporal chaos proposed by Kaneko, which spatially divides the system into various lattices and represents a kind of dynamics evolution both in time and space [6]. There are many types of coupling, e.g., one-way coupling [7], nearest-neighbor coupling [8], global coupling [9], etc. A globally coupled map lattice (GCML) is a discrete time dynamical system where elements interact with all other elements [6,10].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical analysis in controlled globally coupled map lattices

Liang

Jing

2022

Adv Cont Discr Mod

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This paper investigates a globally coupled map lattice. Rigorous proofs to the existence of chaos in the sense of both Li–Yorke and Devaney in two controlled globally coupled map lattices are presented. In addition, the existence of Li–Yorke chaos and Devaney chaos for a general discrete dynamical system in ${\mathbf {R}}^{N}$ R N and $l^{\infty}$ l ∞ is considered. For illustration, two examples are provided.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamical analysis in controlled globally coupled map lattices

Liang

Jing

2022

Adv Cont Discr Mod

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“…Nonlinear characteristics in natural systems are responsible for a great variety of possibilities. Spatiotemporal chaos is one of these possibilities [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Since the coupled map lattices (CML) as a spatiotemporal chaotic system was initially proposed in [9], many researches concentrated on coupled map lattices and obtained mature theory.…”

Section: Introductionmentioning

confidence: 99%

“…Since the coupled map lattices (CML) as a spatiotemporal chaotic system was initially proposed in [9], many researches concentrated on coupled map lattices and obtained mature theory. Khellat et al [10] investigated a globally nonlocal couple map lattice of spatiotemporal chaos system. Meherzi et al [11] proposed one-way coupled-map lattices (OCML) of spatiotemporal chaos system.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal chaos in Arnold coupled logistic map lattice

Zhang

Wang

2013

NAMC

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In this paper, we propose a new spatiotemporal dynamics of Arnold coupled logistic map lattice (ACLML). Here, the coupling method between lattices is not a neighborhood coupling but the non-neighborhood of Arnold cat maps. In the proposed system, the criteria such as Kolmogorov–Sinai entropy density and universality, bifurcation diagram, mutual information, space amplitude and space-time diagrams are investigated in this paper. The new features of the proposed system include the lower mutual information between lattices, larger range of parameters for chaotic behaviors, the higher percentage of lattices in chaotic behaviors for most of parameters and less periodic window in bifurcation diagram. These features are more suitable for cryptography. For numerical simulations, we have employed the coupled map lattices system (CML) for comparison. The results indicate that the proposed system has those superior features to the coupled map lattice system (CML). It should be highlighted that the proposed ACLML is a suitable chaotic system for cryptography.

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“…Other investigation of chaotic see, for example, refs. [3,4,9,10] and some references cited therein.…”

Section: Introductionmentioning

confidence: 99%