ABSTRACT The Turing pattern of a population model with cross‐diffusion and prey defense is studied in this paper. According to the existence conditions of the Turing bifurcation, the amplitude equation at the positive equilibrium of the model is derived using the multiscale analysis. By analyzing the topologically equivalent amplitude equation, one finds that cross‐diffusion can induce Turing instability in the population system at the positive equilibrium, resulting in rich pattern dynamics phenomena, such as spot, spot‐stripe mixed, and stripe patterns. The change in the prey defense coefficient triggers the backward Hopf bifurcation, indicating that the prey defense mechanism is beneficial for maintaining the stability of the population system. Finally, the theoretical results are verified numerically.
Ren et al. (Mon,) studied this question.