This paper deals with the existence and nonexistence of nonconstant positive steady-state solutions to a ratio-dependent predator-prey model with diffusion and with the homogeneous Neumann boundary condition. We demonstrate that there exists a 0 (b) satisfying 0 < a 0 (b) < m 1 for 0 < b < m 1 , suc
Stationary patterns for a prey–predator model with prey-dependent and ratio-dependent functional responses and diffusion
✍ Scribed by Mingxin Wang
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 207 KB
- Volume
- 196
- Category
- Article
- ISSN
- 0167-2789
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We study a prey-predator model with nonlinear diffusions. In a case when the spatial dimension is less than 5, a universal bound for coexistence steady-states is found. By using the bound and the bifurcation theory, we obtain the bounded continuum of coexistence steady-states.
A ratio-dependent predator-prey model with time lag for predator is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, nature of equilibria, permanence, and stability are analyzed. We note that for a ratio-dependent system local asymptotic st
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