The Influences Of Allee Effect On The Population Dynamics System Complexity

In recent years, with the intensification of global environmental destruction, the increasing of species loss and the increasingly prominent role of resource issues, human consider more about the sustainable application of resources and the recycling problems of renewable resources, especially for the development and utilization of biological resources, which is more likely to be extinction by the inappropriate development. On the other hand, a larger number of experiments and studies and field observations indicate that, Allee effect is widespread in the ecosystem, and endangered species are more easily affected by the Allee effect. Allee effect is a destabilizing factor in species persistence, and will largely increase the possibility of the species local extinction, even its global extinction. Furthermore, harvesting is more sensitive in the population with Allee effect, which has been caused wide public concern by the ecologists and conservation biologists. In addition, the evolution of population cooperative behavior is one of the most important theoretical propositions in population evolutionary biology. The cooperative evolution with Allee effect on human beings has not caused wide public concern. The subject of this dissertation is in the population dynamics, which are new focus and not deeply involved in recent years. Firstly, we discussed the raise, evolution and application of Allee effect. Secondly, we established the new predator-prey system with harvesting and Allee effect, which was based on the predator-prey system with positive effect on the prey. Finally, we analyzed the influence of Allee effect on the cooperation of a single-species. By discussing the existence and stability of equilibria, and numerical simulation, we studied how Allee effect impact on the system. The results show that,(1)In the predator-prey dynamic system with Holling type-IV functional response, there was periodic oscillations between the two-species due to the large predation positive effect. The system reached to a stable equilibrium with the decrease of positive effect. However, if the carrying capacity of prey was increased, predator was extinction due to the natural defenses of prey.(2)The appropriate harvesting could increase the stability of the system, and make the system reach to a steady state more easily, and delay the appearance of bifurcation and chaos. The biological economic equilibrium point and optimal capture strategies is given by apply the stability and Pontryagin maximum principle.(3)The system need more time tend to a steady state from an unstable state due to the influence of the strong Allee effect. The system appeared periodic oscillations while the Allee effect was increased. When the Allee effect was increased again, prey was present negative growth and the population tended to local extinction, which leaded the system tend to crash. However, when the system was affected by the weak Allee effect, the system was easier to teach equilibrium. Although the growth rate of prey population is reduced, it still remained positive.(4)In a predator-prey system with harvest and weak Allee effect on prey, the system presented oscillation phenomenon with the increase of Allee effect, and the oscillation frequency is more and more bigger when the Allee effect is more and more stronger. For the original equilibrium system, the system will take more time reach to steady state due the weak Allee effect.(5) Allee effect can easily make species extinct in the bad environmental conditions. However, in the relative superior environmental conditions, the rise of cooperation could be much easier due to Allee effect. As Allee effect is more and more strong, it could promote cooperative evolution more and more advantageously. When the value of Allee effect was greater than a threshold value, the population eventually tended to extinct.