Identification of critical interactions in uncertain network systems with complex dynamics

In this paper, we propose a novel approach based on tools from system theory and ergodic theory of dynamical systems for the identification of critical interactions responsible for the emergence of complex dynamics in network systems. We consider a network system with multiple uncertain random parameters and operating in non-equilibrium. The objective is to determine which of these multiple parameters are critical for maintaining the stability of non-equilibrium dynamics. We provide necessary condition, expressed in terms of variance of uncertainty and nominal system dynamics, to maintain the stability of network system. The condition is used for rank ordering uncertain parameters and to provide margin of stability for network system. The proposed method is applied for the identification of parameters responsible for limit cycle oscillations in biochemical network involved in yeast cell glycolysis and for robust synchronization in network of Kuramoto oscillators with uncertainty in coupling parameters.