Journal
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
Volume 15, Issue -, Pages -Publisher
EDP SCIENCES S A
DOI: 10.1051/mmnp/2019044
Keywords
Herd behavior; predator-prey model; Hopf bifurcation; prey escaping; spatial diffusion
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In this paper, we consider a new approach of prey escaping from herd in a predator-prey model with the presence of spatial diffusion. First, the sensitivity of the equilibrium state density with respect to the escaping rate has been studied. Then, the analysis of the non diffusive system was investigated where boundedness, local, global stability, Hopf bifurcation are obtained. Besides, for the diffusive system, we proved the occurrence of Hopf bifurcation and the non existence of diffusion driven instability. Furthermore, the direction of Hopf bifurcation has been proved using the normal form on the center manifold. Some numerical simulations have been used to illustrate the obtained results.
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