Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 30, Issue 5, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127420500741
Keywords
Predator prey system; Leslie Gower model; Beddington DeAngelis functional response; Hopf bifurcation; nonlocal competition; spatially nonhomogeneous pattern
Funding
- National Natural Science Foundation of P. R. China [11671123]
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In this paper, we present the theoretical results on the pattern formation of a modified Leslie-Gower diffusive predator-prey system with Beddington-DeAngelis functional response and nonlocal prey competition under Neumann boundary conditions. First, we investigate the local stability of homogeneous steady-state solutions and describe the effect of the nonlocal term on the stability of the positive homogeneous steady-state solution. Lyapunov-Schmidt method is applied to the study of steady-state bifurcation and Hopf bifurcation at the interior of constant steady state. In particular, we investigate the existence, stability and multiplicity of spatially nonhomogeneous steady-state solutions and spatially nonhomogeneous periodic solutions. Furthermore, we present a simple description of the dynamical behaviors of the system around the interaction of steady-state bifurcation curve and Hopf bifurcation curve. Finally, a. numerical simulation is provided to show that the nonlocal competition term can destabilize the constant positive steady-state solution and lead to the occurrence of spatially nonhomogeneous steady-state solutions and spatially nonhomogeneous time-periodic solutions.
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