Spatiotemporal dynamics in a toxin-producing predator–prey model with threshold harvesting - Ye, Luhong; Zhao, Hongyong; Wu, Daiyong (Nonlinear Analysis: Modelling and Control, 2023)
In this paper, we propose a toxin-producing predator–prey model with threshold harvesting and study spatiotemporal dynamics of the model under the homogeneous Neumann boundary conditions. At first, the persistence property of solutions to the system is investigated. Then the explicit requirements for the existence of nonconstant steady state solutions are derived by studying the relevant characteristic equation. These steady states occur from related constant steady states via steady state bifurcation. Throughout the analysis of the amplitude equations of Turing pattern by the multiple scale method, pattern formation can be found. Finally, we display  umerical simulations to verify the theoretical outcomes.
Keywords: Turning instability; bifurcation; nonconstant steady state; toxicity; threshold harvesting