Abstracts

Rationale: There is now growing evidence that the global dynamics of neuron networks is not only influenced by intrinsic and synaptic properties but also by the underlying network topology. Networks usually range between regular and random configurations, and it is only recently that intermediate configurations (e.g. small-world networks) have been observed to underly a variety of natural systems, including the brain. However, the functional impact of such network topologies particularly in epilepsy is not well understood. We here investigate the influence of different topologies on the global synchronization of neuron networks. Methods: We investigate the dynamical behavior of networks of pulse-coupled model neurons. We consider coupling schemes that interpolate between regular lattices and random networks depending on the fraction p of rewired connections. The dynamics of each neuron is kept simple to allow for large arrangements. A probability for spontaneous firing is introduced to ensure sustained activity in the network. Results: The neuron networks exhibit very different behaviours. For small p (lattice-like structures) the network exhibits spiral and cyclic waves, which lead to a constant summed activity. For large p (random-like structures) and above a critical coupling strength we observe periodic summed activities, which we connote with global synchronization of the neurons. The transition between the different network behaviors for increasing p is non-continuous. We identify a critical fraction of rewired connections that constitutes a balance between short-ranged connections favoring waves and long-ranged connections favoring global synchronization. Conclusions: Besides the coupling strength, the network topology has a crucial impact on the global synchronization of neuron networks. Our model study indicates that a network topology that features more long-ranged or less short-ranged connections can possibly be regarded as another factor supporting the generation of highly synchronized activities as can be observed during epileptic seizures.