With Pulse Fertility Pest Model The Dynamic Behavior Of The Research

It is well known that pests are the great enemies to crops, and huge damages are caused to crops due to pests every year. To control the pests, it is necessary to understand the growth and development as well as the behavior of them. We know that the adults usually spawn at a particular time of each generation, and consequently the larva is born at a specific time. Therefore, the knowledge of timing of chemical control applications and of the different effects to different ages of the pest are critical factors to the success of pest control.Based on the classical stage-structured population models with birth pulse, in the second chapter of this thesis, we consider the effects of different chemical control tactics on successful pest control. In particular, we assume that the pesticides can only kill larvae pests, or only kill adult pests or both, then we have following quite general model for pest control with chemical control where the maturity rate is δ(δ>0), d(d>0) denotes the death rate, b represents the birth rate of the mature population, Tk+q=τk+1,0≤Pk<1,0≤sk<1, k=1,2,…, q, Z+={0,1,2,…}, pk and sk denote the kill rates of immature and mature populations for the k-th pesticide application, respectively. Note that if pk=0, then it is said that pesticides have no effect on immature population, and if Sk=0then we assume that pesticides have no effect on mature population. For the above model, by studying the discrete dynamical system determined by stroboscopic map we obtained an analytical formula of periodic solution of the system with birth pulses and threshold conditions for its stability. Also, the optimal timing of spraying insecticides in a cycle (m, m+1] was discussed in terms of minimization the threshold value, and the complex dynamical behavior of system was investigated by numerical bifurcation analysis.In nature, due to the changing of external environment, the birth rate or mor-tality rate of the pest populations should be the periodic functions. If so our model proposed in above can be extended as following non-autonomous stage structured model as follows: where d1(t) and d2(t) are the death rate functions of the immature and mature populations, respectively, δ(t) denotes the mature rate function of the mature pop-ulation with d1(t)=d1(t+1), d2(t)=d2(t+1),δ(t)=δ(t+1),0≤pk<1, and0≤Sk<1. The biological means of those parameters are the same as those in the first model. Consequently, the dynamic behavior and biological implications of the above model is analyzed and addressed.