Self-reproducing dynamics in a two-dimensional discrete map

Li, Chunlai; Chen, Zhe; Yang, Xuanbing; He, Shaobo; Yang, Yongyan; Du, Jianrong

doi:10.1140/epjs/s11734-021-00182-1

Cited by 15 publications

(6 citation statements)

References 40 publications

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“…Two kinds of chaotic systems have always been concerned by researchers. The first one has state diversity, such as multistability [20], initial-boosting [21], selfreproducing [22,23] and infinite equilibrium or no equilibrium [24]. The second one possesses structural diversity, such as multi-scroll or multi-cavity attractors [25].…”

Section: Introductionmentioning

confidence: 99%

Unified multi-cavity hyperchaotic map based on open-loop coupling

Li,

Min

et al. 2024

Nonlinear Dyn

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Multi-cavity chaotic map is an important candidate for designing encryption communication system due to its fast iteration speed and complex dynamical behavior. Therefore, it is of great significance to design a simple and unified scheme to implement multicavity attractor. In this paper, a unified multi-cavity hyperchaotic map (UMCHM) is constructed based on open-loop coupling, which features distinct advantages over closed-loop multi-cavity map for its simpler structure and higher sensitivity to initial value. It is found that different shapes of the cavity can be obtained in the UMCHM by altering the type of boundary function, and that the geometric features of the cavity, such as its size, number and location, can be regularly affected by the system parameters. In addition, two controllers are respectively employed to trigger the geometry modulation of cavity on the horizontal axis and extend the cavity space in the vertical direction to form grid multicavity. Next, the influence of cavity geometry and cavity modulation on the spectral entropy is investigated, which provides an important basis for the complexity optimization of UMCHM. Finally, UMCHM is implemented by employing DSP-based hardware platform.

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Section: Introductionmentioning

confidence: 99%

Unified multi-cavity hyperchaotic map based on open-loop coupling

Li,

Min

et al. 2024

Nonlinear Dyn

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“…[35,36] Very recently, extreme multi-stability of nonlinear maps has received much attention. [37][38][39][40] In Ref. [37], Zhang et al presented a class of 2D chaotic maps with extreme multi-stability by introducing a sine term.…”

Section: Introductionmentioning

confidence: 99%

“…Li et al constructed a 2D map with a sine function to show the selfreproducing dynamics of the map, i.e., reproducing infinitely many coexisting attractors of the same structure but in a different position in Ref. [40].…”

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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“…The more variables and parameters, the larger the key space of the high-dimensional chaotic map and the more complex the structure. At the same time, orbit estimation and parameter prediction are more difficult, so they are more suitable for cryptography applications and secure communications [27,28]. Motivated by the above analysis, we construct a class of fractional-order highdimensional hyperchaotic maps based on Gauss maps to explore more complex dynamics.…”

Section: Introductionmentioning

confidence: 99%

A class of fractional-order discrete map with multi-stability and its digital circuit realization

Liu¹,

Mou²,

Jahanshahi³

et al. 2022

Phys. Scr.

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In this paper, a class of nonlinear functions and Gaussian function are modulated to construct a new high-dimensional discrete map. Based on Caputo fractional-order difference definition, the fractional form of the map is given, and its dynamical behaviors are explored. The three discrete maps with different nonlinear functions are compared and analyzed by bifurcation diagrams and Lyapunov exponents, especially the dynamical phenomena that evolve with the order. In addition, the maps have multiple rich stability, including homogeneous and heterogeneous coexistence attractors and hyperchaos coexistence attractors. The spectral entropy (SE) algorithm is used to measure the complexity of one-dimensional and two-dimensional maps. Performance tests show that the fractional-order map has more complex dynamics than the original map. Finally, the new maps were successfully implemented on the digital platform, which shows the simplicity and feasibility of the map implementation. The experimental results provide a reference for the research on the multi-stability of fractional discrete maps.

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Self-reproducing dynamics in a two-dimensional discrete map

Cited by 15 publications

References 40 publications

Unified multi-cavity hyperchaotic map based on open-loop coupling

Unified multi-cavity hyperchaotic map based on open-loop coupling

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

A class of fractional-order discrete map with multi-stability and its digital circuit realization

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