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- Title
The stability and Hopf bifurcation of ratio-dependent predator-prey system with diffusion.
- Authors
ZHANG Tao
- Abstract
The ratio-dependent predator-prey diffusion system is studied. In order to investigate the stability of the positive constant steady state and Hopf bifurcation, the system at the positive constant steady state is linearized and the associated characteristic equation is analyzed, and the asymptotic stability of the positive equilibrium is obtained. It is proved that the positive constant steady state loses stability as the delays cross certain values. The existence of Hopf bifurcation is obtained.
- Subjects
STABILITY theory; HOPF bifurcations; PREDATION; MATHEMATICAL models of diffusion; MATHEMATICAL proofs; TIME delay systems
- Publication
Basic Sciences Journal of Textile Universities / Fangzhi Gaoxiao Jichu Kexue Xuebao, 2012, Vol 25, Issue 3, p314
- ISSN
1006-8341
- Publication type
Article