Study On A Predator-prey System With Impulsive State Feedback Control

It is well-known that the theory of impulsive differential equation is not only richer than the corresponding theoryof differential equation but also represent more natural framework for mathematical modelling of many real world phenomena. In this thesis we establish some population dynamical models concerning harvest behavior about a popula-tion (predators or prey), In mathematically we use the theory of semi-continuous dynamical system to globally investigate dynamical behaviors including the existence and stability of periodic solution. From the biological point of view, the mathematical results are full of biological meanings and can be used to provide policy-making basis for human production and life.We find the sufficient condition for the existence, uniqueness and the orbitally asymptot-ical stability of the order1periodic solutions of the system by differential equation geometry theory and the method of successor functions. Secondly, we prove that the system does not exist order k(k≥2) periodic solution. Finally, some numerical simulations and biological explanations are given.