Abstract
Community structure and interaction delays are common features of ensembles of network coupled oscillators, but their combined effect on the emergence of synchronization has not been studied in detail. We study the transitions between macroscopic states in coupled oscillator systems with community structure and time delays. We show that the combination of these two properties gives rise to non-monotonic transitions, whereby increasing the global coupling strength can both inhibit and promote synchronization, yielding both desynchronization and synchronization transitions. For relatively wide parameter choices we also observe asymmetric suppression of synchronization, where communities compete to suppress one another's synchronization properties until one or more win, totally suppressing the others to effective incoherence. Using the ansatz of Ott and Antonsen we provide analytical descriptions for these transitions that confirm numerical simulations.
Highlights
Understanding the emergence of collective behavior in ensembles of interacting dynamical systems remains an important area of research in the nonlinear dynamics community because of synchronization’s central role in a wide range of phenomena [1,2]
Despite the possible presence of both time delays and community structure in a number of real-world systems with synchronization properties, e.g., bacteria [10,11], power grids [12,13], and brain dynamics [15,16], the collective dynamics that emerge from their combination in heterogeneous systems has to date remained relatively unexplored
We have demonstrated that the combination of these two important properties in coupled oscillator systems gives rise to a rich landscape of dynamical phenomena that does not arise from either of these property in isolation
Summary
Understanding the emergence of collective behavior in ensembles of interacting dynamical systems remains an important area of research in the nonlinear dynamics community because of synchronization’s central role in a wide range of phenomena [1,2]. Examples from both natural and engineered systems include cardiac pacemaker dynamics [3], power grids [4], and Josephson junctions [5].
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