Bifurcation Analysis Of Neutral Delay Logistic Model

In nature, the inherent law and development trend of the population could be grasped through the establishment of mathematical models. The history state of the system provide the necessary information for the development of the present state which is called the phenomenon of time delay.And the joint of the neutral made the project deeper study. In this paper, the types of single time delay and double time delays of neutral type discrete Logistic system are discussed, including the existence,uiqueness and stability and direction of bifurcations of these two models are includes.Considering the impact of the single neutral, in chapter two, a class of neutral type disrete Logistic system with single time delay is investigated.Firstly, the sufficient conditions for the local asymptotic stability of the positive equilibrium are achieved based on the theory of characteristic value and Jury criterion. Secondly, by choosing the intrinsic rate as the bifurcation parameter and using bifurcati-on theory and the center manifold theorem, we get that the discrete model undergoes a flip bifurcation at an exception value of the bifurcation parameter. Finally, numerical examples carry out to justify the main results in this work.Further more, considering the impact of the double neutral, in chapter three, a class of neutral type disrete Logistic system with double time delay is investigated.Some sufficient conditions for the local asymptomatic stability of the equilibrium have been provided by employing Jury criterion. Further, the existences of Flip and N-S bifurcations are discussed by using center manifold theorem and bifurcation theory, and we briefly address the necessary and sufficient conditions for the existence of F-N-S bifurcation. By fitting the population data set of Chinese population from 1981 to 2010 we determine the parameter values, which allows us to evaluate the proposed model and discuss the control strategy for controlling the population in China.