Spectral Analysis of Synchronization in Mobile Networks

Abstract

Abstract. We here analyze a system consisting of agents moving in a two-dimensional space that interact with other agents if they are within a finite range. Considering the motion and the interaction of the agents, the system can be understood as a network with a time-dependent topology. Dynamically, the agents are assumed to be identical oscillators, and the system will eventually reach a state of complete synchronization. In a previous work, we have shown that two qualitatively different mechanisms leading to synchronization in such mobile networks exist, namely global synchronization and local synchronization, depending on the parameters that characterize the oscillatory dynamics and the motion of the agents [1]. In this contribution we show that the spectral pattern differs between the two synchronization mechanisms. For global synchronization the spectrum is flat, which means that all eigenmodes contribute identically. For local synchronization, instead, the synchronization dynamics is determined mostly by the eigenmodes whose eigenvalues are close to zero. This result suggests that the global synchronization mechanism achieves fast synchronization by efficiently using the fast decaying eigenmodes (larger eigenvalues).

Synchronization of mobile chaotic oscillator networks

“…5(a). For noise free non-chaotic systems, 28,29 K converges to a certain value for the small s P limit, but in the present case, where the internal dynamics is chaotic, it diverges. As we increase s P , the time scale of the topology change is faster than that of the oscillator dynamics and K is well approximated by FSA.…”

“…In the opposite case, deviation from FSA caused by local synchronization is studied for the two asymptotic cases d ( d c and d ) d c . This procedure is an extension of the previous studies 28,29 to the case where the local dynamics shows the chaotic behavior.…”

“…In our previous studies, 28,29 we have shown that the synchronization mechanism depends on the dominant time scales, namely, one of the oscillator dynamics and one of the motion of agents. For the case of the non-chaotic oscillators, 28,29 the time scale of the oscillator dynamics is different below and above the percolation transition (d ¼ d c ) 43,44 of the instantaneous topology.…”

“…For the case of the non-chaotic oscillators, 28,29 the time scale of the oscillator dynamics is different below and above the percolation transition (d ¼ d c ) 43,44 of the instantaneous topology. We consider three asymptotic cases individually: derivation of FSA when the time scale of the topology change is much shorter than the oscillator dynamics.…”

“…25 Another one is the analysis using the Fokker-Planck equation formalism when the population of agents is dense and arranged in a ring. 27 In our recent studies, 28,29 we have introduced a conceptual model for synchronization of non-chaotic mobile oscillator networks where agents perform random walks in a two-dimensional (2D) plane. We have found two different mechanisms leading to synchronization, namely, local and global synchronization, depending on the parameter values.…”