Modeling and Dynamics of Interactive Mobile Systems

In this work, we study the dynamics of mobile oscillators in networks with variable topology, an approachthat is more representative of natural and biological systems than traditional stationary networks. We develop a modelin which each node combines an external state, corresponding to an agent moving in a two-dimensional space, andan internal state described by a chaotic oscillator. Our study focuses on three areas: the formulation of a generalframework for simulating these networks, the analysis of the amplification phenomenon in a multilayer network withunidirectional interactions, and the introduction of relative mobility between layers in order to measure its impact onoverall dynamics. Using tools such as the order parameter, the master stability function, Lyapunov theory, andsynchronization error, we show that certain intra- and inter-layer connectivity parameters govern the emergence ofcollective behaviors such as phase synchronization, complete synchronization, or cluster formation. Furthermore, theprobability of obtaining amplified synchronization varies nonlinearly with the amplification coefficient. This work thusproposes a new framework for the study of mobile systems and demonstrates its relevance for understandingcomplex dynamics observed in real- world contexts.

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