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We investigate numerically the collective dynamical behavior of pulse-couplednon-leaky integrate-and-fire-neurons that are arranged on a two-dimensionalsmall-world network. To ensure ongoing activity, we impose a probability forspontaneous firing for each neuron. We study network dynamics evolving fromdifferent sets of initial conditions in dependence on coupling strength andrewiring probability. Beside a homogeneous equilibrium state for low couplingstrength, we observe different local patterns including cyclic waves, spiralwaves, and turbulent-like patterns, which -- depending on network parameters --interfere with the global collective firing of the neurons. We attribute thevarious network dynamics to distinct regimes in the parameter space. For thesame network parameters different network dynamics can be observed depending onthe set of initial conditions only. Such a multistable behavior and theinterplay between local pattern formation and global collective firing may beattributable to the spatiotemporal dynamics of biological networks.

Multistability, local pattern formation, and global collective firing in a small-world network of non-leaky integrate-and-fire neurons