Analysis Of A Class Of Commensalism And Allelospoly Model

Any population in nature is influenced by another. Since nature is complex, interaction among species may not be limited to a single kind. For example, silky ant and aphid compete for resources and habitat in certain environment. However, in the competition, aphid pro-duces honeydew, which offers energy to silky ant and has no negative influence on itself. As a result, the interaction between the two species is commensalism, or single-beneficial. The model, featuring competing and commensalism in certain environment, can be called com-mensalism and allelospoly model. This essay focuses on analysis of the model. Chapter one gives introduction and background knowledge of the essay. Chapter two introduces the model without delay as well as the model delay. Besides, it introduces the conditions of the the balance points being stability of the latter model, combining with continuous dynamic sys-tem and delay differential equation theories. In chapter three, commensalism and allelospoly model with impulse is established. With some theories of impulsive differential equations so that the positive and boundedness of the model is proven, and sufficient condition for the system enduring is also obtained.