Controlling Hyperchaos

Controlling hyperchaos

For a finite-dimensional dynamical system, whose governing equations may or may not be analytically available, we show how to stabilize an unstable orbit in a neighborhood of a "fully"unstable fixed point (i.e., a fixed point at which all eigenvalues of the Jacobian matrix have modulus greater than unity). Only one of the unstable directions is to be stabilized via time-dependent adjustments of...

Controlling hyperchaos in a novel hyperchaotic system

Abstract. The control problem of a novel hyperchaotic system is investigated. The linear, speed, nonlinear, nonlinear doubly-periodic function feedback controls are used to suppress hyperchaos to unstable equilibrium. Limit cases of doubly-periodic function are considered and the hyperbolic function and trigonometric function feedback control laws are derived. The Routh–Hurwitz criterion is app...

Hyperchaos Synchronization Usinggbm

This paper presents synchronization of a new autonomous hyperchaotic system. The generalized backstepping technique is applied to achieve hyperchaos synchronization for the two new hyperchaotic systems. Generalized backstepping method is similarity to backstepping. Backstepping method is used only to strictly feedback systems but generalized backstepping method expands this class. Numerical sim...

Controlling Hyperchaos and Synchronization of an Uncertain Modified Hyperchaotic Lü System

This paper investigates the adaptive control and synchronization of an uncertain modified hyperchaotic Lü system recently discovered by Wang, Zhang, Zheng and Li (2006). This paper deploys nonlinear control for controlling the hyperchaos of the modified hyperchaotic Lü system with unknown parameters and then synchronizing two identical modified hyperchaotic Lü systems with unknown parameters. F...

Heteroclinic loops leading to hyperchaos