Abstract
Neurological disorders such as epileptic seizures are believed to be caused by neuronal synchrony. However, to ascertain the causal role of neuronal synchronization in such diseases through the traditional approach of electrophysiological data analysis remains a controversial, challenging, and outstanding problem. We offer an alternative principle to assess the physiological role of neuronal synchrony based on identifying structural anomalies in the underlying network and studying their impacts on the collective dynamics. In particular, we focus on autapses - time delayed self-feedback links that exist on a small fraction of neurons in the network, and investigate their impacts on network synchronization through a detailed stability analysis. Our main finding is that the proper placement of a small number of autapses in the network can promote synchronization significantly, providing the computational and theoretical bases for hypothesizing a high degree of synchrony in real neuronal networks with autapses. Our result that autapses, the shortest possible links in any network, can effectively modulate the collective dynamics provides also a viable strategy for optimal control of complex network dynamics at minimal cost.
Highlights
Neurological disorders such as epileptic seizures are believed to be caused by neuronal synchrony
This leads to a related question: suppose epileptic seizures are associated with synchronization in small scale neuronal networks, what characteristic structural features do the networks possess to promote or suppress synchrony? Identification of unusual and unconventional features in the seizure network structure which predominately affect synchronization can potentially lead to a deep understanding of the interplay between seizure and synchrony
Implementing a widely studied nonlinear neuron model on complex networks of different topologies, we assume the existence of autapses on a small fraction of the neurons and investigate quantitatively how global synchronization of the network is affected by the locations, strength, and time delays of the autapses
Summary
Neurological disorders such as epileptic seizures are believed to be caused by neuronal synchrony. For our neuronal network with autapses, the stable region depends on the coupling strength parameter and the time delay.
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