Rössler-network with time delay: Univariate impulse pinning synchronization

Abstract

Rössler had a brilliant and successful life as a scientist, during which he published a benchmark dynamical system by using an electronic circuit interpreting chemical reactions. This is our contribution to honour his splendid erudite career. It is a hot topic to regulate a network behavior using the pinning control with respect to a small set of nodes in the network. Besides pinning to small number of nodes, small perturbation to the node dynamics is also demanded. In this paper, the pinning synchronization of coupled Rössler-Network with time delay using univariate impulse control is investigated. Using the Lyapunov theory, a theorem is proved for the asymptotic stability of synchronization in the network. Simulation is given to validate the correctness of the analysis and the effectiveness of the proposed univariate impulse pinning controller.