Chaotic firing in the sinusoidally forced leaky integrate-and-fire model with threshold fatigue

The leaky integrate-and-fire (LIF) model is one of the elementary neuronal models that has been widely used to gain understanding of the behavior of many excitable systems. The sinusoidally forced standard leaky integrate-and-fire model reproduces the quasiperiodic and phase locked discharge trains observed experimentally in neurons. However, this basic model fails to generate chaotic firing, whereas this form of behavior has been observed experimentally. We modify the standard LIF through the introduction of threshold fatigue responsible for progressive decrease of excitability during high frequency firing, as observed experimentally. We show that the dynamics of this neuron model under sinusoidal forcing are governed by the iterates of an annulus map and derive expressions for its two characteristic Lyapunov exponents. Using these exponents, it is shown that chaotic dynamics are possible for this model, unlike the standard leaky integrate-and-fire model. Chaotic dynamics occur when memory effects are strong and only under certain forms of threshold fatigue.