State-dependent effective interactions in oscillator networks through coupling functions with dead zones
arXiv:1904.00626 · doi:10.1098/rsta.2019.0042
Abstract
The dynamics of networks of interacting dynamical systems depend on the nature of the coupling between individual units. We explore networks of oscillatory units with coupling functions that have "dead zones", that is, the coupling functions are zero on sets with interior. For such networks, it is convenient to look at the effective interactions between units rather than the (fixed) structural connectivity to understand the network dynamics. For example, oscillators may effectively decouple in particular phase configurations. Along trajectories the effective interactions are not necessarily static, but the effective coupling may evolve in time. Here, we formalize the concepts of dead zones and effective interactions. We elucidate how the coupling function shapes the possible effective interaction schemes and how they evolve in time.
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- Multi-Population Phase Oscillator Networks with Higher-Order Interactions
- Low-dimensional description for ensembles of identical phase oscillators subject to Cauchy noise
- Chaos in Coupled Heteroclinic Cycles and its Piecewise-Constant Representation
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