Ratio-dependent Competitive Growth Of Two Species In Limited Resource Environment

Biomathematics is a new discipline between mathematics and life science. Originated from1920s, multi-species population dynamics is one of the most important fields in biomathematics and plays an important role in ecology. The study of two species competing for a limited resource in environment is the basis of multi-species population dynamics and provides a theoretical basis for more complex relationships among species. This thesis studied ratio-dependent competitive growth of two species in limited resource environment. It is composed of five chapters.In Chapter1, we reviewed the relationship between species, including com-petition, predation, parasitism and mutualism. Then, we reviewed some basic models in population dynamics and microbial kinetics. Finally, we introduced the resource ratio theory.In chapter2, we built the basic model (2.1) based on the theory of micro-bial kinetics firstly. Then by assuming that only one species is ratio-dependent, we obtained the general solutions of the model and discussed the dynamics of the special solutions numerically.In Chapter3, by assuming that both of the two species are ratio-dependent, we obtained the general solutions of the new model and discussed the dynamics of the special solutions numerically.In chapter4, we studied the growth of the first species in limited resource environment. Then by assuming that the second species is a new one in the en-vironment, we compared its competitive effects based on the results in chapter 2and3, respectively.In chapter5, we pointed out the shortage of the paper and potential applications of the model.