A kind of binary scaling function projective lag synchronization of chaotic systems with stochastic perturbation

Xu, Yuhua; Xie, Chengrong; Qing, Xia

doi:10.1007/s11071-014-1349-6

Cited by 7 publications

(3 citation statements)

References 29 publications

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“…Since the fundamental chaotic financial models proposed in the literature from [31][32][33][34][35][36][37], like the Kaldorian model is listed at [31] and the IS-LM model as [32,33], the hyperchaotic financial model is considered as [34]; moreover, the other nonlinear dynamical models are cited at [35][36][37]. External uncertainties arising from different environmental factors can cause the destabilization of chaotic financial systems and lead to undesirable effects [38][39][40]. e global stabilization and synchronization of chaotic financial systems in the presence of external uncertainty are necessary and have been the topic of excellent research works [41,42].…”

Section: Introductionmentioning

confidence: 99%

Synchronization and Antisynchronization of Identical 4D Hyperchaotic Financial System with External Perturbation via Sliding Mode Control Technique

et al. 2022

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In this article, complete synchronization and antisynchronization in the identical financial chaotic system are presented. The proposed control strategies depend on first-order sliding mode and adaptive integral sliding mode for complete synchronization and antisynchronization of the identical financial chaotic system. In the primary case, the system parameters should be known, and first-order sliding mode control is utilized for synchronization and antisynchronization while in the second case, the system parameters are considered unknown. An adaptive integral sliding mode control strategy is utilized for synchronization and antisynchronization of the system considering the parameters unknown. The error system is changed into a particular structure containing a nominal part and several unknown terms to utilize the adaptive integral sliding mode control. Then, this error system is stabilized using integral sliding mode control. The stabilizing controller is usually developed based on the nominal part plus the compensator control part. To suppress the high-frequency oscillation (chattering) phenomenon, smooth continuous compensator control can be used rather than conventional discontinuous control. The compensator controller along with the adapted law is derived such that the time derivative of the Lyapunov function becomes strictly negative. The effectiveness of the proposed method was tested through computer simulations. The proposed control strategies are verified for that Identical 4D hyperchaotic financial system to attain complete synchronization and antisynchronization along with the improved performance.

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Section: Introductionmentioning

confidence: 99%

Synchronization and Antisynchronization of Identical 4D Hyperchaotic Financial System with External Perturbation via Sliding Mode Control Technique

et al. 2022

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“…Furthermore, research on synchronization and control of the chaos system is particularly topical for decades [11][12][13]. And, people came to know about the value of achieving control of chaos systems in finite time in some domains of engineering.…”

Section: Introductionmentioning

confidence: 99%

Fixed-Time Synchronization of the New Single-Parameter Chaotic System

et al. 2020

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This paper advances a new single-parameter chaotic system with a simple structure, and some basic dynamic behavior of the new single-parameter system is discussed, such as equilibria, dissipativity, the existence of an attractor, Lyapunov exponent, Poincaré map, spectrum map, and bifurcation diagram. Moreover, a new fixed-time convergence theorem is proposed for general chaotic systems based on finite-time control theory, and a fixed-time controller is also put to achieve synchronization of the new chaotic system. Simulation results are presented to show the effectiveness of the theoretical results. The conclusion of the paper is useful for the nonlinear economics and engineering application.

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“…It is well known that economic chaotic systems are inevitably influenced by external disturbances stemmed from environmental interference [17][18][19][20][21][22], and external disturbances may lead to the destabilization of economic and financial chaotic systems and cause undesirable results. It is necessary to study the global stabilization of economic and financial chaotic systems under the presence of external disturbance.…”

Section: Introductionmentioning

confidence: 99%

Chaos Synchronization of Financial Chaotic System with External Perturbation

Xie

Tong

2015

Discrete Dynamics in Nature and Society

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This paper investigates the problem of two kinds of function projective synchronization of financial chaotic system with definite integration scaling function, which are not fully considered in the existing research. Different from the previous methods, in this paper, the following two questions are investigated: (1) two kinds of the definite integration scaling function projective synchronization are given; (2) the upper and lower limit of the definite integral scaling function are the bound dynamical systems. Finally, illustrative example is provided to show the effectiveness of this method.

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A kind of binary scaling function projective lag synchronization of chaotic systems with stochastic perturbation

Cited by 7 publications

References 29 publications

Synchronization and Antisynchronization of Identical 4D Hyperchaotic Financial System with External Perturbation via Sliding Mode Control Technique

Synchronization and Antisynchronization of Identical 4D Hyperchaotic Financial System with External Perturbation via Sliding Mode Control Technique

Fixed-Time Synchronization of the New Single-Parameter Chaotic System

Chaos Synchronization of Financial Chaotic System with External Perturbation

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