Understanding noise-controlled 2D bistable switch by approximating 1D potential

Abstract

The potential landscape is an effective tool for describing the nonequilibrium behaviour of multistable system in the phase space. We estimate the 1D potential of a 2D bistable genetic switch model, which is used to understand the noise-controlled bistable switching behaviours. In the additive noise-induced switching, the distinct difference in residential time attributes to the different potential heights of the two states, and lower potential heights allow more frequently switching between two states. Furthermore, the unsymmetric multiplicative noises could change the residential time significantly through modulating the potential height of the state, where the modulated potential height could be obtained through implementing small noise approximation on the noises. The study confirms that the 1D potential of 2D bistable system could be used to understand noise-induced switching.