Abstract
We discuss synchronization and desynchronization transitions in networks of delay-coupled excitable systems. These transitions arise in response to varying the balance of excitatory and inhibitory couplings in a small-world topology. To describe the local dynamics, we use generic models for type-I excitability, which arises close to a saddle-node bifurcation on an invariant cycle (SNIC or SNIPER), and for type-II excitability, which occurs close to a Hopf bifurcation (FitzHugh-Nagumo model). For large delay times both type-I and type-II systems behave in a similar way. This is different for small delay times, where in case of type-I excitability we find novel multiple transitions between synchronization and desynchronization, when the fraction of inhibitory links is increased. In contrast, only a single desynchronization transition occurs for the FitzHugh-Nagumo model (type-II excitability) for all values of the delay time.
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Schöll, E., Lehnert, J., Keane, A., Dahms, T., Hövel, P. (2016). Control of Desynchronization Transitions in Delay-Coupled Networks of Type-I and Type-II Excitable Systems. In: Wunner, G., Pelster, A. (eds) Selforganization in Complex Systems: The Past, Present, and Future of Synergetics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-27635-9_3
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