Subsystem resetting of a heterogeneous network of theta neurons

Abstract

Stochastic resetting has shown promise in enhancing the stability and control of activity in various dynamical systems. In this study, we extend this framework to the theta neuron network by exploring the effects of partial resetting, where only a fraction of neurons is intermittently reset. Specifically, we analyze both infinite and finite reset rates, using the averaged firing rate as an indicator of network activity stability. For an infinite reset rate, a high proportion of resetting neurons drives the network to stable resting or spiking states. This process collapses the bistable region at the Cusp bifurcation, resulting in smooth and predictable transitions. In contrast, finite resetting introduces stochastic fluctuations, leading to more complex dynamics that occasionally deviate from theoretical predictions. These insights highlight the role of partial resetting in stabilizing neural dynamics and provide a foundation for potential applications in biological systems and neuromorphic computing.