Existence, Multiplicity, and Stability of Positive Solutions of a Predator-Prey Model with Dinosaur Functional Response

Xiaozhou Feng, Kenan Shi, Jianhui Tian, Tongqian Zhang
2017 Mathematical Problems in Engineering  
We investigate the property of positive solutions of a predator-prey model with Dinosaur functional response under Dirichlet boundary conditions. Firstly, using the comparison principle and fixed point index theory, the sufficient conditions and necessary conditions on coexistence of positive solutions of a predator-prey model with Dinosaur functional response are established. Secondly, by virtue of bifurcation theory, perturbation theory of eigenvalues, and the fixed point index theory, we
more » ... ndex theory, we establish the bifurcation of positive solutions of the model and obtain the stability and multiplicity of the positive solution under certain conditions. Furthermore, the local uniqueness result is studied when b and d are small enough. Finally, we investigate the multiplicity, uniqueness, and stability of positive solutions when k>0 is sufficiently large.
doi:10.1155/2017/4912032 fatcat:ykfaniwb7ffglf2f5ob3x4tham