scholarly journals Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Jie Ran ◽  
Yu-Qin Li ◽  
Shao-Juan Ma ◽  
Juan Wu
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Discrete Time ◽  
Control Method ◽  
Deterministic System ◽  
Hyperchaotic System ◽  
Discrete Time System ◽  
Amplitude Control ◽  
Random Disturbances ◽  
Dynamical Features

The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.

scholarly journals Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1344
Author(s):  
A. Othman Almatroud ◽  
Amina-Aicha Khennaoui ◽  
Adel Ouannas ◽  
Giuseppe Grassi ◽  
M. Mossa Al-sawalha ◽  
...  
Keyword(s):  
Discrete Time ◽  
Software Package ◽  
Control Method ◽  
Approximate Entropy ◽  
Dynamical Analysis ◽  
Largest Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
Discrete Time System ◽  
Time System ◽  
Quadratic Nonlinearities

This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0–1 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package.

scholarly journals Hopf Bifurcation of the Higher Dimensional Hénon Map

2019 ◽  
Vol 67 (1) ◽  
pp. 73-78
Author(s):  
Saiful Islam ◽  
Chandra Nath Podder
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Discrete Time ◽  
Explicit Criterion ◽  
Hénon Map ◽  
Henon Map ◽  
Higher Dimensional ◽  
Generalized Hénon Map

In this paper, the discrete time generalized Hénon map is considered and the existence of Hopf bifurcation via an explicit criterion for N≥3, in particular for N=4 and N=5 has given. The relation between the parameters a and b as well as the range of the values of the parameters for N=3,4,5 has driven and the existence of Hopf bifurcation is demonstrated for the values of the parameters calculated from their relations. The results of numerical simulations for different values of the parameters are also presented. Dhaka Univ. J. Sci. 67(1): 73-78, 2019 (January)

scholarly journals Discretization analysis of bifurcation based nonlinear amplifiers

2017 ◽  
Vol 15 ◽  
pp. 43-47
Author(s):  
Sven Feldkord ◽  
Marco Reit ◽  
Wolfgang Mathis
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Integration ◽  
Discrete Time ◽  
Continuous Time ◽  
Higher Order ◽  
Qualitative Behavior ◽  
Discrete Time System ◽  
Integration Methods ◽  
Numerical Integration Methods ◽  
Nonlinear Amplifiers

Abstract. Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov–Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov–Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge–Kutta methods transform the truncated normalform equation of the Andronov–Hopf bifurcation into the normalform equation of the Neimark–Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark–Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov–Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark–Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.

Chaos Control of the Fractional Order Stochastic Chen System

2013 ◽  
Vol 694-697 ◽  
pp. 2130-2133
Author(s):  
Jie Zheng ◽  
Shao Juan Ma ◽  
Duan Dong
Keyword(s):  
Feedback Control ◽  
Orthogonal Polynomial ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaos Control ◽  
Control Method ◽  
Random Parameter ◽  
Deterministic System ◽  
Chen System ◽  
Control Laws

In this paper, we study chaos control of the fractional order Chen system with the bounded random parameter. Firstly, we transform the fractional order Chen system with random parameter into an equivalent deterministic system by the orthogonal polynomial approximation. Secondly, based on Routh-Hrwitz criterion, the derivative feedback control laws are applied to fractional order equivalent deterministic Chen system. Lastly, numerical simulations show that the control method is effective and feasible.

A New Method for Discrete-Time System Reduction

1988 ◽  
Author(s):  
Ioannis S. Apostolakis ◽  
John Diamessis ◽  
David Jordan
Keyword(s):  
Discrete Time ◽  
New Method ◽  
Discrete Time System ◽  
Time System ◽  
System Reduction
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