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

Abstract:

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 dier. Time delays and coupling strengths between the dierent 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 effect 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].

References

[1] W. Just, A. Pelster, M. Schanz, and E. Schöll, Phil. Trans. R. Soc. A 368, 303 (2010) [1].
[2] L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 80, 2109 (1998) [2].
[3] F. Sorrentino and E. Ott, Phys. Rev. E 76, 056114 (2007) [3].
[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) [4].