Two-Dimensional Memristive Hyperchaotic Maps and Application in Secure Communication

Li, Houzhen; Hua, Zhongyun; Bao, Han; Zhu, Linsheng; Chen, Mo; Bao, Bocheng

doi:10.1109/tie.2020.3022539

Cited by 202 publications

(64 citation statements)

References 32 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: 71%

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: 71%

Extreme Multistability in Simple Area-Preserving Map

Bao

Zhu

et al. 2020

IEEE Access

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“…And it avoids the disadvantage that parameter sensitivity of the continuous nonlinear system, so the discrete system is more concerned in the practical engineering. Inspired by the mathematical model of the continuous memristor, the discussion of discrete memristor becomes a topical issue in recently [20][21][22][23][24][25][26]. He and Peng et al proposed the integer-order and fractional-order discrete memristor mathematical models, and introduced these discrete models into the sine map [20] and two high-dimensional chaotic maps [21,22].…”

Section: Introductionmentioning

confidence: 99%

“…Simulations show that these systems can not only enhance the complexity of the original system, but also have abundant dynamic behaviors such as hyperchaos and coexistence attractors. Bao's group presented several hyperchaotic maps based on the discrete memristor [23][24][25], and verified the numerical results in digital circuits, which laid the foundation for the practical applications of discrete memristor. Kong et al [26] also reported a new discrete memristive chaotic map, and the offset-boosting and amplitude control are discussed in detail by linear transformation.…”

Section: Introductionmentioning

confidence: 99%

Parameter identification for discrete memristive chaotic map using adaptive differential evolution algorithm

Peng

Sun

2021

Nonlinear Dyn

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Since the concept of discrete memristor was proposed, more and more scholars began to study this topic. At present, most of the works on the discrete memristor are devoted to the mathematical modeling and circuit implementation, but the research on its synchronization control has not received much attention. This paper focuses on the parameter identification for the discrete memristive chaotic map, and a modified intelligent optimization algorithm named adaptive differential evolution algorithm is proposed. To deal with the complex behaviors of hyperchaos and coexisting attractors of the considered discrete memristive chaotic maps, the identification objective function adopts two special parts: time sequences and return maps. Numerical simulations demonstrate that the proposed algorithm has the best performance among the six existing algorithms, and it can still accurately identify the parameters of the original system under noise interference.

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“…Chaotic systems have many engineering applications. ey can be used in image encryption [22], communication [23], circuits [24], robots [25], and so on [26]. Field programmable gate array (FPGA) implementation of nonlinear systems plays a vital role in realizing a system using targeted hardware.…”

Section: Introductionmentioning

confidence: 99%

A Novel Megastable Oscillator with a Strange Structure of Coexisting Attractors: Design, Analysis, and FPGA Implementation

Zhang

Vijayakumar²,

Jamal

et al. 2021

Complexity

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Megastable chaotic systems are somehow the newest in the family of special chaotic systems. In this paper, a new megastable two-dimensional system is proposed. In this system, coexisting attractors are in some islands, interestingly covered by megalimit cycles. The introduced two-dimensional system has no defined equilibrium point. However, it seems that the origin plays the role of an unstable equilibrium point. Therefore, the attractors are determined as hidden attractors. Adding a forcing term to the system, we can obtain chaotic solutions and coexisting strange attractors. Moreover, the effect of three different values of the forcing term’s amplitude is studied. The dynamical properties of the designed system are investigated using attractor plots, bifurcation diagrams, and Lyapunov Exponents diagram. Phase portraits of the novel megastable oscillator are presented by FPGA design. Xilinx system generator block diagrams of the proposed system and trigonometric functions are also presented.

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Two-Dimensional Memristive Hyperchaotic Maps and Application in Secure Communication

Cited by 202 publications

References 32 publications

Extreme Multistability in Simple Area-Preserving Map

Extreme Multistability in Simple Area-Preserving Map

Parameter identification for discrete memristive chaotic map using adaptive differential evolution algorithm

A Novel Megastable Oscillator with a Strange Structure of Coexisting Attractors: Design, Analysis, and FPGA Implementation

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