Simple model for 1/f^α noise

We present a simple stochastic mechanism which generates pulse trains exhibiting a power-law distribution of the pulse intervals and a 1/f^α power spectrum over several decades at low frequencies with α close to 1. The essential ingredient of our model is a fluctuating threshold which performs a Brownian motion. Whenever an increasing potential V(t) hits the threshold, V(t) is reset to the origin and a pulse is emitted. We show that if V(t) increases linearly in time, the pulse intervals can be approximated by a random walk with multiplicative noise. Our model agrees with recent experiments in neurobiology and explains the high interpulse interval variability and the occurrence of 1/f^α noise observed in cortical neurons and earthquake data.