Dynamics Of A Plant-herbivore Model With Plant Energy Storage

Taking biology as the background and on the basis of the existing population model,this paper considers the influence of time delay,and analyzes the dynamics of the two types of population models respectively.The main work is as follows:Firstly,the purpose and significance of these two types of population models and their current development are summarized.Determined the main content of this article,at the same time,the basic knowledge needed in the research process is also introduced.Secondly,considering the influence of plant underground parts on plant growth,a plant-herbivore model with plant energy storage is established.Discuss the plant-herbivore model without time delay,use the monotonicity and unevenness of the quadratic function of one variable to analyze the existence of the interior equilibrium.Equilibrium stability can be derived from positive and negative values of the characteristic roots.The stability of the model is considered for interior equilibrium with single and double time delay.Hopf bifurcation theory was used to determine whether there was a periodic solution for the plant-herbivore model with time delay.It is found that when plants store enough energy,it is favorable for plants and herbivores to coexist and use Matlab to numerically simulate the theoretical analysis results.In order to further study the dynamic properties of plants or herbivore population,considering the effect of spatial heterogeneity on population size,a class of time-delayed diffusion single population models with strong Allee effects is established.The dynamic characteristics of single population model under two cases of non-diffusion and diffusion are respectively given.The stability of the equilibrium is also obtained based on the sign of the characteristic roots.The existence of periodic solutions of the Hopf bifurcation is also obtained by taking time delays as bifurcation parameters.Using the normal form method and the central manifold theorem,the direction of the Hopf bifurcation is calculated.The theoretical analysis results are verified and the relationship between the asymptotic behavior of solutions and the initial functions is shown by numerical simulation via Matlab.