Self-exciting chaos as a dynamic model for irregular neural spiking

We introduce a nonlinear dynamical system with self-exciting chaotic dynamics. Its interspike interval return map shows a noisy Poisson-like distribution. Spike sequences from different initial conditions are unrelated but possess the same mean frequency. In the presence of noisy perturbations, sequences started from different initial conditions synchronize. The features of the model are compared with experimental results for irregular spike sequences in neurons. Self-exciting chaos offers a mechanism for temporal coding of complex input signals.