Effect of heterogeneous time delays and link weights on the stability and convergence time of large interconnected dynamical systems: A case study

In this paper, we study the stability (convergence time) of an interconnected dynamical system with respect to its connectivity in the presence of delayed feedbacks sensory inputs/outputs data. In particular, we show that under some conditions, that we introduce and present in this paper, related to the interconnected links time-delays, the less connected a given dynamical system is, the longer it will take for the overall system to stabilize. We address the conditions for obtaining an estimate of the convergence time of the system based on the system interconnections weights and time delays. In particular, we study the conditions under which such property is conserved when homogenous and/or heterogeneous time delays are introduced to the links of the interconnected system considered. Analysis of the affect of arbitrary heterogeneous time delays on the dynamical system links, system stability, and convergence time is also presented.