Modeling And Analysis Of Singular System Models With Wheat Aphid Populations Based On Catastrophe Phenomenon

China is the main production areas of wheat planting in the world.Various aphid populations attack the wheat and lead to the yield reduction more than 30%,in some severe reigns,which causes huge losses on the national economy.Based on the above,it has important theoretical and practical significance that the ecology mechanism for the breakout of the aphid populations is studied.In fact,the breakout of the aphid populations is catastrophe movements,and the impulsive behavior of singular systems is also a catastrophe phenomenon.In the paper,two models with two populations and three populations are proposed by using the principles of ecology and considering the influence of biological factors on the aphid population,respectively.Combined the catastrophe with singular theory,the catastrophe phenomenon are studied frown a new view.The main contents are as follows:Firstly,on the basis of the fold catastrophe model of the wheat aphid population,the affect of some biological factors such as the wheat population,is considered to build up a two-dimensional singular system model of the aphid population.The stability of the model are discussed using the stability theory of singular systems and the corresponding sufficient conditions are given.And the ecology mechanism of breakout of the aphid population are investigated by singularity theory.From the view of qualitative analysis,the simulations are carried out to prove the results.Secondly,on the basis of the fold catastrophe model of the wheat aphid population,considering the impact of the wheat population and the enemy population on the wheat,an three-dimensional singular systems model is proposed.The complexity dynamic behaviors of the model are studied,and the corresponding conditions are got.Some simulations are carried out to prove our results.The study above may provide the theoretical basis for the prevention and control of the aphid population.