Seasons Of The Dynamic Behavior Of Two Competing Species Model Impact Analysis

As is known to all, species competition is a common rule in the nature. Com-petition makes species coexistence, also can lead to the survival of the fittest that species evolve to a higher order. Therefore, the study of species competition is very meaningful to the entire ecology.There are many reasons to produce intraspecific competition and interspecific competition, changes in the survival environment is a very important factor in caus-ing competition. Environment changes influence the survival and development of the species, which natural seasons caused environmental change affects not only the growth of the species, and also affect the composition of the species.Lotka (1925) and Volterra (1926) proposed the famous competition model, as follows: Where rt is the net growth rate of the population i, ai is the intraspecific competition rates, α and β are interspecific competition rates. In this paper, based on this model, we consider the seasons influencing on the survival of the species. Assume one year as a period, we define the period of time from spring to autumn as a good season due to the warm weather and enough food. In this season, two competitive species with the law of Malthus growth have a good living environment and do not cause competition. Accordingly, from the fall to the spring of the second year is defined as a bad season due to the cold climate and lack of resources, the species is prone to cause the intraspecific and interspecific competition.Therefore, the practical problems can be depicted as following model: Where m∈Z+iλi,ri,ai,α and β are all positive constants,Φ>∈(0,1],λi is the death rate of the population i. By using the theory of matrix and monotone dynam-ical systems, the conditions for the stability and the existence of the zero solution, boundary equilibrium and the interior equilibrium are obtained, i.e., the conditions of the competitive exclusion and competitive existence. We discuss in detail the effects of two death rates in the bad season and the proportion of the good season on the competition outcomes.