| Mathematical biology is an cross discipline between mathematics and biology. Itis based on mathematical methods to solve the problems of biology. and it is studyingtheoretically about mathematical questions and methods in relation to biology. The mainresearch object of the mathematical biology is ecological system. An individual organismwith sports ability could make the corresponding reaction because of the external stimulateis a common phenomenon in ecological system. The property that the movement becauseof reaction has certain direction can be called tendency, there are many common differenttypes of taxis such as chemotaxis, aerotaxis, haptotaxis, phobophototaxis and so on.Thestudy of these tendency not only has the important theoretical significance but also hasmore important practical significance in real life.peasant often use the habits that insectshave tendency to some chemicals to attract and trap the insects in Agriculture . Peoplemake full use of the phobophototaxis of moths to hunt them in the night.The tropism model was first established in 1970 by Segel Keller. This kind of modelhas got widely recognition between domestic and international scholars, of course theresearch of this kind of model also more and more in-depth.The predation model of thispaper fully tendency of behavior which attract people's widely attention.As is known toall, the respondent behavior for surrounding environment of living organisms is the basiclife response,Consider tendency of behavior is one of the important factors to describethe biological systems accurately.So the research of this paper has important practicalsignificance.This paper mainly aims at the predation systems with the behavior of biologicalchemotaxis. for one thing, we introduce the historical background of the problems andprepared knowledge of the paper. Then account for the existence and uniqueness of localsolutions by compression mapping principle. Finally, we will discuss the global existenceof solutions. |
