Anti-Synchronization of the Four-Dimensional Hyperchaotic System with Uncertain Parameters Via Adaptive Control

Jabbari, Azizeh; Kheiri, Hossein

doi:10.1080/1726037x.2012.10698603

Cited by 5 publications

(8 citation statements)

References 14 publications

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“…The complex behavior of system (1) was first noted by Ma and Chen in 2001 [45,46]. Then many papers were published where the dynamics of this model has been investigated by means of various methods and techniques, such as Lyapunov exponents and bifurcation diagrams [22,47]; synchronizations with linear and nonlinear feedbacks [48,49], adaptive [50], sliding mode [51] and passive [51] control methods [51]; control via linear, speed and time-delay feedbacks [52][53][54].…”

Section: Periodic Motionmentioning

confidence: 99%

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Integrability analysis of chaotic and hyperchaotic finance systems

Szumiński

2018

Nonlinear Dyn

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In this paper, we consider two chaotic finance models recently studied in the literature. The first one, introduced by Huang and Li, has a form of three first-order nonlinear differential equationṡ x = z + (y − a)x,ẏ = 1 − by − x 2 ,ż = − x − cz. The second system, called a hyperchaotic finance model, is defined bẏ x = z + (y − a)x + u, z = − x − cz,ẏ = 1 − by − x 2 , u = − dx y − ku. In both models, (a, b, c, d, k) are real positive parameters. In order to present the complexity of these systems Poincaré cross sections, bifurcation diagrams, Lyapunov exponents spectrum and the Kaplan-Yorke dimension have been calculated. Moreover, we show that the Huang-Li system is not integrable in a class of functions meromorphic in variables (x, y, z), for all real values of parameters (a, b, c), while the hyperchaotic system is not integrable in the case when k = c and := 1 + d(a + d − c) > 0. We give analytic proofs of these facts analyzing properties of the differential Galois groups of variational equations along cer-The research has been supported by the National Science Centre of Poland under Grants DEC

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Section: Periodic Motionmentioning

confidence: 99%

“…, ϕ n (t)) be a particular solution of equations (47). Then t −→ ψ(t) := (ϕ(t), 0) ∈ C 2n 52is a particular solution of Hamiltonian system (50). The variational equations along this particular solution are given bẏ…”

Section: Lemmamentioning

confidence: 99%

Integrability analysis of chaotic and hyperchaotic finance systems

Szumiński

2018

Nonlinear Dyn

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“…Consider the following three-dimensional autonomous non-linear chaotic financial system model which consists of production, currency and labor force [23,21,27,22]:…”

Section: State Space Model Of Chaotic Finance Systemmentioning

confidence: 99%

“…The changes of x 1 is in proportion with the rate of average profit margin dx 1 , where d is a proportionality constant and its value can vary within a certain range. Therefore, based on the system (1), a new chaotic finance system can be generated by adding the average profit margin dx 1 , then the new threedimensional autonomous equations for chaotic financial system model has the following form [23,21,27]:…”

Section: State Space Model Of Chaotic Finance Systemmentioning

confidence: 99%

“…Controlling the chaos is more efficient and significant rather than synchronizing the chaos in many chaotic financial systems due to the sensitivity of economics chaos to the initial value. Several studies attempted to develop the control framework for chaotic financial systems [23,24,25,26,27,28,16]. Linear feedback, speed feedback, selection of gain matrix, revision of gain matrix controllers [21], time-delayed feedback controllers [29] and single controller scheme [30] were used for the control of the chaotic financial system.…”

Section: Introductionmentioning

confidence: 99%

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Robust Stabilization of a Non-Linear Chaotic Financial System with Uncertain Parameters

Choudhary

2018

IJET

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The paper investigates an analytical approach for robust stabilization of nonlinear chaotic financial system in the presence of uncertain parameters. The primary focus of this paper is to find a robust solution for quickly adjusting and controlling the interest rate, investment demand and price exponent when the chaotic phenomenon occurs in the financial system or economic crisis happens. The paper fi rst demonstrates the non-linear dynamical model of the chaotic financial system and then it adopts Lyapunov stability theory based adaptive control scheme for robust stabilization of nonlinear chaotic financial system in the presence of uncertain parameters. Numerical simulations are demonstrated to verify the effectiveness of the proposed control scheme. The simulation results of this paper show that control scheme successfully eliminates the chaos of the nonlinear financial systems

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Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

Mobayen

Tchier

2017

Asian Journal of Control

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This paper proposes a new state-feedback stabilization control technique for a class of uncertain chaotic systems with Lipschitz nonlinearity conditions. Based on Lyapunov stabilization theory and the linear matrix inequality (LMI) scheme, a new sufficient condition formulated in the form of LMIs is created for the chaos synchronization of chaotic systems with parametric uncertainties and external disturbances on the slave system. Using Barbalat's lemma, the suggested approach guarantees that the slave system synchronizes to the master system at an asymptotical convergence rate. Meanwhile, a criterion to find the proper feedback gain vector F is also provided. A new continuous-bounded nonlinear function is introduced to cope with the disturbances and uncertainties and obtain a desired control performance, i.e. small steady-state error and fast settling time. Several criteria are derived to guarantee the asymptotic and robust stability of the uncertain master-slave systems. Furthermore, the proposed controller is independent of the order of the system's model. Numerical simulation results are displayed with an expected satisfactory performance compared to the available methods.

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Anti-Synchronization of the Four-Dimensional Hyperchaotic System with Uncertain Parameters Via Adaptive Control

Cited by 5 publications

References 14 publications

Integrability analysis of chaotic and hyperchaotic finance systems

Integrability analysis of chaotic and hyperchaotic finance systems

Robust Stabilization of a Non-Linear Chaotic Financial System with Uncertain Parameters

Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

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