Persistence and periodic orbits of a three-competitor model with refuges.
We consider a model composed of four patches. One patch has three competing species forming a heteroclinic cycle within the patch. The remaining patches are refuges for the three competitors, and each species can diffuse between the competitive patch and its refuge. It is proved that the model can be made persistent by the introduction of the refuges for the competitors even if the isolated competitive patch has an attracting heteroclinic cycle. Further it is shown that Hopf bifurcation is possible when we change the value of the diffusion constant and periodic orbits may exist in a specific case.
Takeuchi
Y
Y
Department of Applied Mathematics, Faculty of Engineering, Shizuoka University, Hamamatsu, Japan.
Oshime
Y
Y
Matsuda
H
H
D000818:Animals; D005399:Fishes; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D010507:Periodicity; D011157:Population Dynamics