Model Analysis Of Diffusion Herbs And Herbivore With Logistic Growth And Regrowth

In recent years,there have been a lot of studies on predation models,but there are few models considering the effects of underground parts on plant growth.The traditional biological model plants mostly grow in the form of Logistic,but the roots of plants in nature have the ability of regeneration.Therefore,considering the influence of aboveground and underground parts of plants on the biological population,this paper studied the diffuse herbaceous plants and plant eaters with Logistic growth and re-growth based on this,and the main work is as follows:Firstly,the background and current situation of this research were summarized,and the model of diffuse herbaceous plants and plant eaters with Logistic growth and re-growth was established.The main research contents of this paper were briefly introduced.Secondly,the dynamic properties of space homogeneous systems are studied.The dissipation and durability of the positive solution of the system are proved by the comparison theorem of ordinary differential equations.Then,the stability of the equilibrium solution is analyzed by using the Hurwitz discriminant method and constructing Lyapunov function.Finally,the theorem is verified by numerical simulation.Thirdly,the dynamic properties of space inhomogeneous systems are studied.The dissipation and persistence of positive solutions are discussed by means of the comparison theorem of parabolic equations.Then the stability of equilibrium solutions is analyzed by using Hurwitz discriminant method and constructing Lyapunov function.Secondly,using Harnack inequality and Poincare inequality,we investigate the existence and non-existence of nonconstant steady-state solutions,and analyze the effects of the underground parts of plants on the dynamic properties of the system.Finally,the theorems are verified by numerical simulation.