Dynamic analysis and multistability of a novel four-wing chaotic system with smooth piecewise quadratic nonlinearity

Signing, V. R. Folifack; Kengne, Jacques; Kana, L. K.

doi:10.1016/j.chaos.2018.06.008

Cited by 37 publications

(6 citation statements)

References 48 publications

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“…On the other hand, sliding mode control suffers from chattering, and the disturbances are also supposed to be matched [81]. Besides, most of synchronizers based on hyperchaotic systems found in the literature employ complete actuation [8], [53], [83], [84]. Then, the main peculiarity of our work, in contrast to the literature, thus lies in that neither matching condition nor fully-actuated control is assumed.…”

Section: Remarkmentioning

confidence: 98%

Secure Communication Based on Hyperchaotic Underactuated Projective Synchronization

Gularte¹,

Alves²,

Vargas³

et al. 2021

IEEE Access

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This paper proposes a scheme for secure telecommunication based on the projective synchronization of hyperchaotic systems. The design of the synchronizer considers the presence of disturbances to increase the robustness of the method. The main advantage of the proposed approach lies in that only two control inputs are required to synchronize the master and slave systems. Hence, the control structure is simple, which, in turn, simplifies the applications. Based on Lyapunov theory, the proposed approach ensures the finite-time convergence of the synchronization error to a small neighborhood of the origin, even in the presence of disturbances in all states. Simulations to both show the advantages and applications of the proposed approach were also accomplished to validate the theory.

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Section: Remarkmentioning

confidence: 98%

Secure Communication Based on Hyperchaotic Underactuated Projective Synchronization

Gularte¹,

Alves²,

Vargas³

et al. 2021

IEEE Access

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Section: Introductionmentioning

confidence: 99%

“…A class of chaotic systems are characterized by the coexistence of many different types of attractors, a phenomenon referred to as multistability which has become a very important research topic and received much attention recently [43][44][45][46]. In [44], a smooth piecewise quadratic nonlinear four-wing chaotic system is proposed. When the appropriate parameters including a two-wing and four-wing chaotic attractor are selected, the system can observe four kinds of unconnected coexisting stable states under different initial values and show rich dynamic behaviors.…”

Section: Introductionmentioning

confidence: 99%

Multistability Analysis, Coexisting Multiple Attractors, and FPGA Implementation of Yu–Wang Four-Wing Chaotic System

Liu

Shen

et al. 2020

Mathematical Problems in Engineering

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In this paper, we further study the dynamic characteristics of the Yu–Wang chaotic system obtained by Yu and Wang in 2012. The system can show a four-wing chaotic attractor in any direction, including all 3D spaces and 2D planes. For this reason, our interest is focused on multistability generation and chaotic FPGA implementation. The stability analysis, bifurcation diagram, basin of attraction, and Lyapunov exponent spectrum are given as the methods to analyze the dynamic behavior of this system. The analyses show that each system parameter has different coexistence phenomena including coexisting chaotic, coexisting stable node, and coexisting limit cycle. Some remarkable features of the system are that it can generate transient one-wing chaos, transient two-wing chaos, and offset boosting. These phenomena have not been found in previous studies of the Yu–Wang chaotic system, so they are worth sharing. Then, the RK4 algorithm of the Verilog 32-bit floating-point standard format is used to realize the autonomous multistable 4D Yu–Wang chaotic system on FPGA, so that it can be applied in embedded engineering based on chaos. Experiments show that the maximum operating frequency of the Yu–Wang chaotic oscillator designed based on FPGA is 161.212 MHz.

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“…Through the above method, Miranda and Stone (1993) first proposed the generation of multi-wing attractor in Lorenz system in 1993. After that, a large number of four-wing chaotic systems have been reported (Lin et al, 2016;Signing et al, 2018;Xie et al, 2017). Especially in the past decade, a class of four-wing chaotic systems with more complex dynamic behaviors were proposed.…”

Section: Introductionmentioning

confidence: 99%

One-to-four-wing hyperchaotic fractional-order system and its circuit realization

Wen

2020

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Purpose This paper aims to introduce a novel 4D hyperchaotic fractional-order system which can produce one-to-four-wing hyperchaotic attractors. In the study of chaotic systems with variable-wing attractors, although some chaotic systems can generate one-to-four-wing attractors, none of them are hyperchaotic attractors, which is incomplete for the dynamic characteristics of chaotic systems. Design/methodology/approach A novel 4D fractional-order hyperchaotic system is proposed based on the classical three-dimensional Lü system. The complex and abundant dynamic behaviors of the fractional-order system are analyzed by phase diagrams, bifurcation diagrams and the corresponding Lyapunov exponents. In addition, SE and C0 algorithms are used to analyze the complexity of the fractional-order system. Then, the influence of order q on the system is also investigated. Finally, the circuit is implemented using physical components. Findings The most particular interest is that the system can generate one-to-four-wing hyperchaotic attractors with only one parameter variation. Then, the hardware circuit experimental results tally with the numerical simulations, which proves the validity and feasibility of the fractional-order hyperchaotic system. Besides, under different initial conditions, coexisting attractors can be obtained by changing the parameter d or the order q. Then, the complexity analysis of the system shows that the fractional-order chaotic system has higher complexity than the corresponding integer-order chaotic system. Originality/value The circuit structure of the fractional-order hyperchaotic system is simple and easy to implement, and one-to-four-wing hyperchaotic attractors can be observed in the circuit. To the best of the knowledge, this unique phenomenon has not been reported in any literature. It is of great reference value to analysis and circuit realization of fractional-order chaotic systems.

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Dynamic analysis and multistability of a novel four-wing chaotic system with smooth piecewise quadratic nonlinearity

Cited by 37 publications

References 48 publications

Secure Communication Based on Hyperchaotic Underactuated Projective Synchronization

Secure Communication Based on Hyperchaotic Underactuated Projective Synchronization

Multistability Analysis, Coexisting Multiple Attractors, and FPGA Implementation of Yu–Wang Four-Wing Chaotic System

One-to-four-wing hyperchaotic fractional-order system and its circuit realization

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