Dynamical analysis and fixed-time synchronization of a chaotic system with hidden attractor and a line equilibrium

Tian, Huaigu; Wang, Zhen; Zhang, Hui; Cao, Zelin; Zhang, Peijun

doi:10.1140/epjs/s11734-022-00553-2

Cited by 15 publications

(7 citation statements)

References 48 publications

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“…Another used control is adaptive control with complete error or anti-synchronization, where they focus on the time of convergence of the error in the synchronization [ 29 ] or the problem where the system parameters are unknown [ 30 , 31 , 32 , 33 , 34 ]. Another control proposal is the fixed-time synchronization observer , which emphasizes the time of convergence of the error in the synchronization under complete error [ 35 ]. Finally, another control, back-stepping control , synchronizes two different systems with complete error by setting an extra variable [ 36 ].…”

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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“…As a nonlinear dual-port element, memristor is added to the classical nonlinear system, such as Chua's circuit [13], Lorenz system [14], and Chen's system [15]. Te memristor circuit composed of various classical nonlinear circuits shows colorful and unforgettable dynamic behaviors, including hidden attractors [16][17][18], hyperchaotic behaviors [19], symmetric attractors [13], and extreme multistability [20][21][22][23] with infnite number of coexistence attractors. Te memristor model described by piecewise linear function [24], quadratic nonlinear function [25], and cubic nonlinear function [26] is a mathematical model often used by scholars.…”

Section: Introductionmentioning

confidence: 99%

“…It can be seen from the previous description that the multistability of memristor chaotic system brings many advantages in engineering; however, it will also lead to some undesirable things due to the "minor to damage" characteristics of chaos. In the past, scholars have proposed different control schemes to achieve the synchronization of memristor chaotic systems as follows: fnite time synchronization schemes [16,[32][33][34][35]and fxed time synchronization schemes [18,36,37]. In addition, these proposed synchronization schemes require the same controller input dimension as the system dimension, which makes the controller more complex, and synchronization time cannot be given.…”

Section: Introductionmentioning

confidence: 99%

Complex Dynamic Analysis, Circuit Design and Simplified Predefined Time Synchronization for a Jerk Absolute Memristor Chaotic System

et al. 2023

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In this parper, a 4D absolute memristor Jerk chaotic system is proposed. Firstly, complex dynamics are studied by phase diagram, Poincaré section, power spectrum, bifurcation diagram, 0-1 test, and Lyapunov exponent spectrum. Then, the period doubling bifurcation, degradation, and offset boosting are revealed. For the feasibility of practical application, the analog circuit and FPGA digital circuit are designed. Finally, a simplified predefined time synchronization scheme is proposed; comparing with the full control input synchronization scheme, the simplified predefined time synchronization scheme can not only reduce the controller inputs but also predefine the synchronization time.

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“…Chaotic synchronization can be used to achieve signal encryption at the sending end and undistorted recovery at the receiving end thanks to the sensitive initial values and noise-like properties of chaos. At present, the main methods for achieving chaos synchronization include the master-slave synchronization method [29,30], generalized synchronization method [31], the phase synchronization method [32], etc. In fact, the proportion factor between the master and slave systems determines the type of chaotic synchronization.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Analysis and Misalignment Projection Synchronization of a Novel RLCM Fractional-Order Memristor Circuit System

Liu,

Tian,

Wang

et al. 2023

Axioms

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In this paper, a simple and novel fractional-order memristor circuit is established, which contains only resistance, inductance, capacitance and memristor. By using fractional calculus theory and the Adomian numerical algorithm, special bifurcations, chaotic degradation, C0 and Spectral Entropy (SE) complexity under one-dimensional and two-dimensional parameter variations with different orders, parameters and initial memristor values of the system were studied. Meanwhile, in order to better utilize the applications of fractional-order memristor systems in communication and security, a misalignment projection synchronization scheme for fractional-order systems is proposed, which overcomes the shortcomings of constructing Lyapunov functions for fractional-order systems to prove stability and designing controllers for the Laplace transform matrix.

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Dynamical analysis and fixed-time synchronization of a chaotic system with hidden attractor and a line equilibrium

Cited by 15 publications

References 48 publications

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Complex Dynamic Analysis, Circuit Design and Simplified Predefined Time Synchronization for a Jerk Absolute Memristor Chaotic System

Dynamical Analysis and Misalignment Projection Synchronization of a Novel RLCM Fractional-Order Memristor Circuit System

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