Ecological Models on Multi Species Interaction within Unlimited Resources
Tóm tắt
In this paper, we present a three species food web system in that two species are interacting mutually and a third species, which is a predator to the first species and host for the second species i.e. there is a commensalism interaction between second and third species. All three species considered in unbounded availability of natural resources. The analytical investigations of this ecological model are observed by employing known direct methods if not by numerical methods. This model is characterized by a system of first order nonlinear ordinary coupled differential equations. We investigate three cases: (1) The death rate of any one (say third species) species is greater than its birth rate. (2) The death rates of any two species (say second, third) are greater than their birth rates. (3) The death rates of all the species are greater than their birth rates. Further the local stability at existing equilibrium points and global stability by suitable parametric values to the model equations are examined. The numerical simulations are supporting the analytical findings. As a whole we can conclude that the ecological food systems involving such kind of interactions may exist for a long time under certain environmental conditions.
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