Desynchronization and chaotification of nonlinear dynamical systems
The subject of the paper is the system of maps \(x_{n+1}=M_n(x_n)\), \(y_n=M_n(y_n) + N_n\), where \(x_n, y_n \in \mathbb{R}^{n}\) and \(N_n\in \mathbb{R}^{n}\) is some control function, which is chosen to be zero when \(x_n=y_n\). The author suggests a specific form for the control \(N_n\) that makes the synchronized state \(x=y\) unstable and dynamics of the system chaotic. The goal is achieved by choosing \(N_n\) in such a way that the equation for `error' becomes splitted from the other variables and, moreover, it has the form \(\xi_{n+1}=\delta \xi_n \mod \varepsilon\) with some positive \(\delta\) and \(\varepsilon\). The result generalizes the method of \textit{G. Chen} and \textit{D. Lai} [Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, 1585-1590 (1998; Zbl 0941.93522)].
scientific article; zbMATH DE number 1965095