Chaos control in Shimizu Morioka system by Lie algebraic exact linearization
نویسندگان
چکیده
منابع مشابه
Shimizu-morioka Chaotic System
This paper derives new results for the adaptive control and synchronization design of the Shimizu-Morioka chaotic system (1980), when the system parameters are unknown. First, we build an adaptive controller to stabilize the Shimizu-Morioka chaotic system to its unstable equilibrium at the origin. Then we build an adaptive synchronizer to achieve global chaos synchronization of the identical Sh...
متن کاملDynamics of Linear Bidirectional Synchronization of Shimizu-Morioka chaotic system
The Shimizu-Morioka dynamical system is a Lorentz-like system that is of much importance in fields like fluid dynamics and laser physics. This paper proposes an identical synchronization scheme for generalized linearly bidirectionally coupled chaotic Shimizu-Morioka dynamical system. Lyapunov stability theory is applied to establish the conditions on coupling parameters for synchronization. Num...
متن کاملThe Hopf Bifurcation in the Shimizu-morioka System
We study the local Hopf bifurcations of codimension one and two which occur in the Shimizu-Morioka system. This system is a simplified model proposed for studying the dynamics of the well known Lorenz system for large Rayleigh numbers. We present an analytic study and their bifurcation diagrams of these kinds of Hopf bifurcation, showing the qualitative changes in the dynamics of its solutions ...
متن کاملOutput Regulation of Shimizu-morioka Chaotic System by State Feedback Control
This paper investigates the problem of output regulation of Shimizu-Morioka chaotic system, which is one of the classical chaotic systems proposed by T. Shimizu and N. Morioka (1980). Explicitly, for the constant tracking problem, new state feedback control laws regulating the output of the Shimizu-Morioka chaotic system have been derived using the regulator equations of C.I. Byrnes and A. Isid...
متن کاملAnalytic Exact Upper Bound for the Lyapunov Dimension of the Shimizu-Morioka System
In applied investigations, the invariance of the Lyapunov dimension under a diffeomorphism is often used. However, in the case of irregular linearization, this fact was not strictly considered in the classical works. In the present work, the invariance of the Lyapunov dimension under diffeomorphism is demonstrated in the general case. This fact is used to obtain the analytic exact upper bound o...
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ژورنال
عنوان ژورنال: International Journal of Dynamics and Control
سال: 2013
ISSN: 2195-268X,2195-2698
DOI: 10.1007/s40435-013-0051-8