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Lou, Y. and Winkler, M. (2015) Global Existence and Uniform Boundedness of Smooth Solutions to a Cross-Diffusion System with Equal Diffusion Rates. Communications in Partial Differential Equations, 40, 1905-1941.
https://doi.org/10.1080/03605302.2015.1052882

has been cited by the following article:

• TITLE: Numerical Simulation of Predator-Prey Patterns in Marine Organisms

  AUTHORS: Shuai Zhang, Zhiyuan Li

  KEYWORDS: Linear Stability, Nine-Point Difference Method, Weakly Nonlinear Analysis

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.5, May 28, 2025

  ABSTRACT: This paper mainly investigates the application of predator-prey systems. By deriving the first-order principles of the stochastic partial differential equations, we analyzed the stability of the model at the equilibrium point. The coefficients of the outgoing amplitude equation were deduced using the Wakefield nonlinear analysis. The model was numerically simulated by setting parameters using the nine-point difference method, and the simulation results are in agreement with the numerical results. In addition, a marine predator-prey model combining the fear effect and refuge environment is proposed in this paper, and the pattern formation mechanism of species coexistence is revealed through theoretical analysis and numerical simulation.