Transient Phase Clusters in a Two-Population Network of Kuramoto Oscillators with Heterogeneous Adaptive Interaction

Abstract

Adaptive interactions are an important property of many real-word network systems. A feature of such networks is the change in their connectivity depending on the current states of the interacting elements. In this work, we study the question of how the heterogeneous character of adaptive couplings influences the emergence of new scenarios in the collective behavior of networks. Within the framework of a two-population network of coupled phase oscillators, we analyze the role of various factors of heterogeneous interaction, such as the rules of coupling adaptation and the rate of their change in the formation of various types of coherent behavior of the network. We show that various schemes of heterogeneous adaptation lead to the formation of transient phase clusters of various types.

Complex Networks and Interacting Particle Systems

“…On the other hand, within fixed scales (in particular, at the molecular scale), network analyses of structure tend to either take data-analytic approaches [18,19] or impose external "control parameters" [8] built on the notion of adaptive links [20]. In this context, a change in temperature which allows certain molecular structures to emerge would be modeled by setting an external parameter which regulates how the links are created and destroyed.…”