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Cluster synchronization and inhibition-induced desynchronization in complex networks with time-delayed coupling


Time delays arise naturally in many complex networks, for instance in neural networks, as delayed coupling or delayed feedback due to nite signal transmission and processing times [1]. We study synchronization and desynchronization in delay-coupled neural networks, using a master stability function approach [2, 3].

We extend the framework of the master stability function to more complex synchronization patterns where the nodes are synchronized in groups with phase lags between the groups [4]. The local dynamics of each group can di er. Time delays and coupling strengths between the di erent clusters can be chosen freely. Using the master stability function approach reduces the M-cluster state to an M-dimensional synchronization manifold corresponding to a system of M coupled nodes. The time delays and coupling strengths between clusters are reflected in the coupling between these M nodes allowing for complex dynamics within the synchronization manifold like bursting patterns.

For homogeneous delay and coupling strength, we nd that zero-lag synchronization is always stable if all couplings are excitatory. We study the e ffect of introducing inhibitory links in random or regular rings of excitatory coupled nodes, the latter yielding a small-world-like architecture. The inhibition leads to a transition to desynchronized networks as the number of inhibitory links approaches a critical value. This critical value crucially depends on the topology of the underlying excitatory network [5].



[1] W. Just, A. Pelster, M. Schanz, and E. Schöll, Phil. Trans. R. Soc. A 368, 303 (2010).
[2] L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 80, 2109 (1998).
[3] F. Sorrentino and E. Ott, Phys. Rev. E 76, 056114 (2007).
[4] T. Dahms, J. Lehnert, and E. Schöll, in preparation (2012).
[5] J. Lehnert, T. Dahms, P. Hövel, and E. Schöll, EPL 96, 60013 (2011).

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