A new 5-D hyperchaotic four-wing system with multistability and hidden attractor, its backstepping control, and circuit simulation

Vaidyanathan, Sundarapandian; Sambas, Aceng; Azar, Ahmad Taher; Rana, K.P.S.; Kumar, Vineet

doi:10.1016/b978-0-12-817582-8.00013-1

Cited by 13 publications

(3 citation statements)

References 44 publications

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“…This control intentionally fails when synchronizing Chua’s system with hidden attractors to show that the existence of hidden attractors significantly affects synchronization [ 15 ]. Another control is sliding mode control (SMC) with complete error or anti-synchronization [ 25 , 26 , 27 , 28 ]. However, this control requires studying and understanding the theory, which has strong mathematical foundations.…”

Section: Related Workmentioning

confidence: 99%

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Zaqueros-Martinez

Gómez

Tlelo‐Cuautle

et al. 2023

Entropy

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Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi–Sugeno (T–S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance.

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Section: Related Workmentioning

confidence: 99%

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Zaqueros-Martinez

Gómez

Tlelo‐Cuautle

et al. 2023

Entropy

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“…Another kind of attractor newly proposed in recent years was called hidden attractor, whose basin does not intersect with the small neighborhood of any equilibrium points. The coexisting attractors and hidden attractors are of considerable importance in nonlinear dynamics and engineering applications [26][27][28][29][30][31][32]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Dynamics analysis of memristor chaotic circuit with coexisting hidden attractors

Dou,

Guo,

et al. 2024

Eur. Phys. J. Plus

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In this paper, a novel Sr 0.97 Ba 0.03 TiO 3−δ memristor based fifth-order chaotic circuit was proposed. A new cubic nonlinear magnetic control model was established by analyzing the measured data. The equilibrium points and its stability of the circuit system were analyzed by the Jacobi matrix method, and the effects of the initial states and circuit parameters on the system were discussed though methods of Lyapunov exponents spectra, bifurcation diagrams, phase diagrams, and poincaré maps. The results show that the chaotic circuit can produce complex dynamic phenomena with the variation of initial states and circuit parameters. The dynamic phenomena such as coexisting attractors have been discovered. In particular, coexisting hidden attractors were generated in the chaotic circuit, which was of great significance in engineering applications.

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“…Wang et al [7] characterized a-new-uniform-four-dimensionaluniform-hyperchaotic-Lorenz-type system, employing a bifurcation method and Lyapunov stability theory. Compared to ordinary chaotic systems, hyperchaotic systems have more potential applications in information security [8][9][10][11][12], finance [13,14], lasers [15][16][17], and circuits [18][19][20][21]. Due to their higher dimensionality, hyperchaotic systems are accompanied by a vast amount of randomness and unpredictability.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation, Periodic Solutions, and Control of a New 4D Hyperchaotic System

Zhou

Guo

2023

Mathematics

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In this paper, a new four-dimensional (4D) hyperchaotic biplane system is designed and presented. The dynamical properties of this new system are studied by means of tools such as bifurcation diagrams, Lyapunov exponents and phase diagrams. The Hopf bifurcation and periodic solutions of this hyperchaotic system are solved analytically. In addition, a new hyperchaotic control strategy is applied, and a comparative analysis of the controlled system is performed.

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A new 5-D hyperchaotic four-wing system with multistability and hidden attractor, its backstepping control, and circuit simulation

Cited by 13 publications

References 44 publications

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Dynamics analysis of memristor chaotic circuit with coexisting hidden attractors

Hopf Bifurcation, Periodic Solutions, and Control of a New 4D Hyperchaotic System

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