Bifurcation and stability analysis of cognitive populations in toxic environments

Abstract

This paper focuses on the dynamic behavior of a single-species model with two cognitive perceptual functions in a toxic environment, to simulate the different responses of fish to environmental changes. We first performed a spectral analysis of the model to obtain an eigenvalue problem for the stability of the constant steady state solution of the model. Then, Turing bifurcation analysis and Hopf bifurcation analysis for linear and nonlinear perceptual function models are studied. The results show that the model with linear perceptual function exhibit both kinds of bifurcations, but the model with nonlinear perceptual function only exhibits Turing bifurcations, which is novel in the field of biological mathematics. In view of biology point, the nonlinear perception function suggests that fish individuals share information among themselves and update their memories, whereas the linear perception function does not share this characteristic. Numerical simulations verify our analysis results.