Information Flow In A Network Of Nonlinear System Under Bidirectional Asymmetric Coupling

Abstract

Exploration and understanding of the dynamics of complex networks are always important in the research of various disciplines. Most of the complex networks, used for experimental demonstration, employ biological or electronic systems. But, experiments using biological or real neuronal systems are extremely difficult and expensive. So, one has to work with nonlinear electronic systems as a prototypical model. But mostly studied networks employed symmetric coupling. In engineering and biological applications, asymmetric coupling is more general and practical. In this paper, we investigate the dynamics of one dimensional network of digital phase-locked loops (DPLLs) with bidirectional asymmetric coupling. DPLLs are unavoidable electronic units widely used in communication engineering and computer hardware. We consider both local and nonlocal coupling and identify several distinct spatiotemporal patterns. We map all patterns on parameter space to grab complete network dynamics. Detail stability analyses for both local and mnonlocal asymmetric coupling are carried out. Analytical zone of network synchronization completely matches with the simulation results. In case of local coupling, the most important and extraordinary spatiotemporal dynamics is the traveling random pattern (TRP). We estimate traveling velocities of TRP for different parameter values and identify its functional dependence on the degree of asymmetry in coupling. It is discovered that, TRP follows some special initial conditions. Motivating by this notion, we explore that; employing TRP, one can transmit encoded information through the network. For this, one has to fed information in the form of initial condition to the network. A new measure is proposed, called average relative local deviation that effectively discriminates between synchronous and asynchronous spatiotemporal patterns in the network.