Hyperchaos in Wilson–Cowan oscillator circuits

Abstract

The Wilson–Cowan equations were originally shown to produce limit cycle oscillations for a range of parameters. Others subsequently showed that two coupled Wilson–Cowan oscillators could produce chaos, especially if the oscillator coupling was from inhibitory interneurons of one oscillator to excitatory neurons of the other. Here this is extended to show that chains, grids, and sparse networks of Wilson–Cowan oscillators generate hyperchaos with linearly increasing complexity as the number of oscillators increases. As there is now evidence that humans can voluntarily generate hyperchaotic visuomotor sequences, these results are particularly relevant to the unpredictability of a range of human behaviors. These also include incipient senescence in aging, effects of concussive brain injuries, autism, and perhaps also intelligence and creativity. NEW & NOTEWORTHY This paper represents an exploration of hyperchaos in coupled Wilson–Cowan equations. Results show that hyperchaos (number of positive Lyapunov exponents) grows linearly with the number of oscillators in the array and leads to high levels of unpredictability in the neural response.