Controlling chaos with periodic parametric perturbations in Lorenz system

Wu, Zheng-Mao; Xie, Jin; Fang, Yanyan; Xu, Zhi-Hong

doi:10.1016/j.chaos.2005.10.060

Cited by 16 publications

(7 citation statements)

References 23 publications

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“…The study of chaotic systems has attracted a lot of attentions in the literature. The chaotic system in a population model is studied in depth by the Lorenz et al [Lorenz (1963[Lorenz ( , 1965[Lorenz ( , 1982; Yassen (2005); Wu, Xie, Fang et al (2007); Zhao, Xing and Yu (2009)]. The chaotic system is characterized by a "sensitive dependence on initial condition" [Lorenz (1963)], such that the predictability of the future state is often severely limited by the chaotic dynamics of the system.…”

Section: Introductionmentioning

confidence: 99%

Numerical Validations of the Tangent Linear Model for the Lorenz Equations

Zhao¹,

Zhang²,

Li³

et al. 2019

Computer Modeling in Engineering &Amp; Sciences

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The validity of the tangent linear model (TLM) is studied numerically using the example of the Lorenz equations in this paper. The relationship between the limit of the validity time of the TLM and initial perturbations for the Lorenz equations is investigated using the Monte Carlo sampling method. A new error function between the nonlinear and the linear evolution of the perturbations is proposed. Furthermore, numerical sensitivity analysis is carried to establish the relationship between parameters and the validity of the TLM, such as the initial perturbation, the prediction time, the time step size and so on, by the method of mathematical statistics.

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Section: Introductionmentioning

confidence: 99%

Numerical Validations of the Tangent Linear Model for the Lorenz Equations

Zhao¹,

Zhang²,

Li³

et al. 2019

Computer Modeling in Engineering &Amp; Sciences

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“…Meanwhile, we will keep on completing the work of Mirus and Sprott [17]. Therefore, in the spirit of perturbing a physically accessible system parameter, the parameter R was perturbed to be R(1 + R 1 sin(ωt)) [8].…”

Section: Introductionmentioning

confidence: 99%

“…The existence of periodic solutions and homoclinic orbits has been researched extensively by Melnikov method developed by Wiggins and Holmes [4,5] and has been proved in some systems [6][7][8]. The one-parameter DLE display rich dynamical behaviors and have been extensively investigated [2].…”

Section: Introductionmentioning

confidence: 99%

Controlling the diffusionless Lorenz equations with periodic parametric perturbation

Wei

Yang

2009

Computers & Mathematics with Applications

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a b s t r a c tDiffusionless Lorenz equations (DLE) are a simple one-parameter version of the wellknown Lorenz model, which was obtained in the limit of high Rayleigh and Prandtl numbers, physically corresponding to diffusionless convection. A simple control method is presented to control chaos by using periodic parameter perturbation in DLE. By using the generalized Melnikov method, the parameter conditions could be obtained to guide the controlled DLE to a low-periodic motion. Moreover, the existence conditions of periodic orbits and homoclinic orbits in the system are given. Some results of the numerical simulation are also explained clearly by a rigorous analysis.

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“…Feedback methods [7]- [11] are used to stabilize the unstable periodic orbit of chaotic systems by feeding back their states. Nonfeedback methods [11]- [14] are adopted to change chaotic behaviors by applying perturbations to some parameters or variables. In the paper, we use feedback method to control the dynamic behavior of Liu system.…”

Section: Introductionmentioning

confidence: 99%

Controlling Liu Chaotic System with Feedback Method and Its Circuit Realization

Wang

2016

IJMNTA

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In the paper, the Liu system with a feedback controller is discussed. The influence of the feedback coefficient of the controlled system is studied through Lyapunov exponents spectrum and bifurcation diagram. Various attractors are demonstrated not only by numerical simulations but also by circuit experiments. Only one feedback channel is used in our study, which is useful in communication. The circuit experiments show that our study has significance in practical applications.

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Controlling chaos with periodic parametric perturbations in Lorenz system

Cited by 16 publications

References 23 publications

Numerical Validations of the Tangent Linear Model for the Lorenz Equations

Numerical Validations of the Tangent Linear Model for the Lorenz Equations

Controlling the diffusionless Lorenz equations with periodic parametric perturbation

Controlling Liu Chaotic System with Feedback Method and Its Circuit Realization

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