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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 . 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 . 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 .
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