Stability analysis of synchronization in long-range temporal networks using theory of dichotomy.

Abstract

Most of the previous studies on the stability analysis of synchronization in static or time-varying networks are based on the master stability function approach, which is a semi-analytical concept. The necessary and sufficient conditions for synchronization in time-varying networks are challenging problems since the last few years. We focus on the stability analysis of synchronization in time-varying networks, particularly long-range networks. The use of dichotomy theory to derive sufficient conditions for synchronization in this context is an interesting approach. The incorporation of long-range interactions adds complexity and might lead to larger regions of synchronization, providing valuable insights into the dynamics of such networks. Analyzing the co-action of the time-varying nature in the network topology and long-range interactions is a relevant and challenging task, especially when the network is not synchronized. This work appears to explore the interplay between these factors and their impact on synchronization. Additionally, the numerical study considering long-range connections governed by a power-law within the framework of an Erdös-Rényi random network is a practical way to validate and test the analytical results. It is good to see that we are exploring the effects of varying parameters such as rewiring probability, coupling strength, and power-law exponent on the synchronization state.