Dynamics Feature and Synchronization of a Robust Fractional‐Order Chaotic System

Abstract

Exploring the dynamics feature of robust chaotic system is an attractive yet recent topic of interest. In this paper, we introduce a three-dimensional fractional-order chaotic system. The important finding by analysis is that the position of signalx3descends at the speed of 1/cas the parameterbincreases, and the signal amplitude ofx1,x2can be controlled by the parametermin terms of the power function with the index −1/2. What is more, the dynamics remains constant with the variation of parametersbandm. Consequently, this system can provide rich encoding keys for chaotic communication. By considering the properties of amplitude and position modulation, the partial projective synchronization and partial phase synchronization are realized with linear control scheme. The distribution map of optimal synchronization region in the control-parameter space is charted by defining the power consumption of controller. Numerical simulations are executed to confirm the theoretical analysis.

Eigenvalue Based Approach for Assessment of Global Robustness of Nonlinear Dynamical Systems

“…What can we say about the asymptotic behavior (as t → ∞) of solutions of perturbed system (1)? This question represents one of the fundamental problems in the area of robust stability and robustness of the systems in general and so the effect of (known or unknown) perturbations on the solutions of nominal system as a potential source of instability attracts the attention and interest of scientific community for a long time in the various contexts, recently for example [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. A comprehensive overview of the most significant results on robust control theory as a stand-alone subfield of control theory and its history is presented in [17,18].…”