Stochastic Stability and Bifurcation for the Selkov Model with Noise

In this paper, we consider a stochastic Selkov model for the glycolysis process. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic mathematical modeling. First, we employ polar coordinate transformation and stochastic averaging method to transform the original system into an Itô averaging diffusion system. Next, we investigate the stochastic dynamical bifurcation of the Itô averaging amplitude equation by studying the qualitative changes of invariant measures and explore the phenomenological bifurcation (P-bifurcation) by using the counterpart Fokker-Planck equation. Finally, some numerical simulations are presented to verify our analytic arguments.