Can hyperchaotic maps with high complexity produce multistability?

Natiq, Hayder; Banerjee, Santo; Ariffin, Muhammad Rezal Kamel

doi:10.1063/1.5079886

Cited by 59 publications

(37 citation statements)

References 16 publications

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“…Importantly, when the number of coexisting multiple attractors goes to infinity, such a coexistence phenomenon is defined as extreme multistability, which is closely relied on the initial conditions and has been reported in many continuous-time dynamical systems [14], [15]. Similarly, the phenomenon of multistability can be also observed in numerous discrete iterative maps of difference equations, including the kicked rotor map [2], bistable Hénon map [16], nonlinear hyperchaotic map [17], three-degree-of-freedom vibroimpact system [18], two-dimensional sine map with initialsboosted coexisting chaos [19], and two-dimensional memristive hyperchaotic maps [20]. However, such an initial condition-relied extreme multistability has not yet been found in a discrete iterative map.…”

Section: Introductionmentioning

confidence: 92%

Extreme Multistability in Simple Area-Preserving Map

Bao

Zhu

et al. 2020

IEEE Access

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Initial condition-relied extreme multistability has been recently found in many continuous dynamical systems. However, such a specific phenomenon has not yet been discovered in a discrete iterative map. To investigate this phenomenon, this paper proposes a two-dimensional conservative map only with one sine nonlinearity. The proposed simple discrete map is area-preserving in the phase space and displays the coexistence of infinite chaotic and quasi-periodic orbits caused by infinite fixed points. Multiple numerical results indicate that the area-preserving chaotic and quasi-periodic orbits have the initial condition-relied quasi-periodic route to chaos and initial condition-boosting bifurcation dynamics, which allow the simple area-preserving map to emerge the complex phenomenon of extreme multistability. Furthermore, a microcontroller-based hardware platform is developed to implement the initial conditionboosting chaotic signals.

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Section: Introductionmentioning

confidence: 92%

Extreme Multistability in Simple Area-Preserving Map

Bao

Zhu

et al. 2020

IEEE Access

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“…(1) e period of LMFSR has no relation with an initial value (2) e different outputs of LMFSR are uncorrelated e maximum period of all these experiments is 65500 when code C � 0203. e whole length of feedback shift register is 16 bits, so the maximum length of the sequence should be 2 16 � 65536.…”

Section: Analysis Of the Experimentmentioning

confidence: 99%

“…However, the performance of the discrete chaotic system degrades because of the finite precision effect. Some research studies do lots of investigation to improve the performance in low-dimensional systems [11][12][13][14] and high-dimension systems [15,16]. Hua et al [13,14] proposed a novel and efficient low-dimensional chaotic system with high complexity.…”

Section: Introductionmentioning

confidence: 99%

Performance of Finite Precision on Discrete Chaotic Map Based on a Feedback Shift Register

Huang

Ding

2020

Complexity

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The scintillating technological improvements have changed the process of communication in all parts of the world. Shopping, banking, instant communication, and so on can be operated online and do not care about the linkage of those Internet communications. Because of simple chaotic structure, discrete nature, less arithmetic computation, and high complexity, low-dimensional chaotic systems such as a logistic map and tent map are more attractive than a high-dimensional chaotic system. To overcome the disadvantages of a low-dimensional chaotic map with a finite precision in chaos-based application, the chaotic map with a feedback shift register (CMFSR) is proposed. The related properties and performance associated with CMFSR are analysed. The relationship among the precision of the system, the architecture, and the performance are discussed. The experiments about new pseudorandom number generator (PRNG) based on CMFSR show that our scheme is simple, secure, and easy to accomplish. Experiments show that the proposed architecture of CMFSR is secure for random number generation.

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“…Similar to the continuous chaotic systems, the discrete chaotic maps are taken as a class of important dynamical systems, which can also give rise to the phenomenon of multistability. In the past decade, the coexistence of double or multiple attractors has been found in the Hénon maps [ 17 , 18 ], the M-dimensional nonlinear hyperchaotic model [ 19 ] and the multistage DC/DC switching converter [ 20 ]. Recently, two types of simple 2D hyperchaotic maps with sine trigonometric nonlinearity and constant controllers were shown to generate initial-boosted infinite attractors along a phase line [ 21 , 22 ].…”

Section: Introductionmentioning

confidence: 99%

Coexisting Infinite Orbits in an Area-Preserving Lozi Map

Chen

et al. 2020

Entropy

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Extreme multistability with coexisting infinite orbits has been reported in many continuous memristor-based dynamical circuits and systems, but rarely in discrete dynamical systems. This paper reports the finding of initial values-related coexisting infinite orbits in an area-preserving Lozi map under specific parameter settings. We use the bifurcation diagram and phase orbit diagram to disclose the coexisting infinite orbits that include period, quasi-period and chaos with different types and topologies, and we employ the spectral entropy and sample entropy to depict the initial values-related complexity. Finally, a microprocessor-based hardware platform is developed to acquire four sets of four-channel voltage sequences by switching the initial values. The results show that the area-preserving Lozi map displays coexisting infinite orbits with complicated complexity distributions, which heavily rely on its initial values.

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Can hyperchaotic maps with high complexity produce multistability?

Cited by 59 publications

References 16 publications

Extreme Multistability in Simple Area-Preserving Map

Extreme Multistability in Simple Area-Preserving Map

Performance of Finite Precision on Discrete Chaotic Map Based on a Feedback Shift Register

Coexisting Infinite Orbits in an Area-Preserving Lozi Map

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