PATTERN FORMATION OF PREY–PREDATOR SYSTEM WITH SCHOOLING BEHAVIOR VIA AMPLITUDE EQUATION

T. Singh, K. Shrivastava, A. Kumar, R. Dubey and V. Narayan Mishra

  DOI:  https://doi.org/10.37418/amsj.9.11.77

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In this paper, we propose and analyze the spatial prey–predator system with schooling behavior. Firstly, we examine the possibility and uniqueness of the coexistence equilibrium solutions of the model. We obtain Turing instability for spatial prey–predator model. By the use of weakly nonlinear analysis near the threshold value of parameter for patterns, we obtain the amplitude equation. Finally, we present numerical outcomes to justify the numerical results. Some interesting patterns shows the spatial dynamical complexity of prey–predator model.

Keywords: Prey–predator system, schooling behavior, pattern formation, amplitude equations, Turing instability.