Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 246, Issue 5, Pages 1944-1977Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2008.10.024
Keywords
Diffusive predator-prey system; Holling type-II functional response; Hopf bifurcation; Steady state bifurcation; Spatially non-homogeneous periodic orbits; Global bifurcation
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Funding
- National Natural Science Foundation of China [10771045, 10671049]
- Doctoral Program of Higher Education
- National Science Foundation of US
- Longjiang Professorship of Department of Education of Heilongiiang Province
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A diffusive predator-prey system with Holling type-II predator functional response subject to Neumann boundary conditions is considered. Hopf and steady state bifurcation analysis are carried out in details. In particular we show the existence of multiple spatially non-homogeneous periodic orbits while the system parameters are all spatially homogeneous. Our results and global bifurcation theory also suggest the existence of loops of spatially non-homogeneous periodic orbits and steady state solutions. These results provide theoretical evidences to the complex spatiotemporal dynamics found by numerical simulation. (c) 2008 Elsevier Inc. All rights reserved.
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