A Kinetic Study Of Two Types Of Plant-herbivore Models

In the preceding decades,research results on the predator-prey model have become more and more abundant.However,there are few models that consider both underground growth and multi-population competition defense.In fact,the plant-herbivore model incorporating multiple factors is not only more consistent with the actual plant growth and population survival,but also has an important impact on the diversity of species in the ecosystem.Based on this,the dynamic properties of two types of plant-herbivore models with underground growth of plants are studied in this paper.Firstly,we briefly summarize the research background and research status of the subject,and consider two species plant-herbivore model and three species plantherbivore model,and also list the research contents of this paper.Secondly,the two species plant-herbivore model with underground growth of plants is considered.With the help of the normal form and the center manifold theory,the existence of Hopf bifurcation and the stability of bifurcation periodic solutions are proved.Some numerical simulations are carried out to illustrate our results.Finally,the three species plant-herbivore model incorporating underground growth and competition of plants is studied.By using the comparison theorem of ordinary differential equations,we prove the positivity and boundedness of solutions,by means of eigenvalue theory and Lyapunov function,the existence and stability of equilibria are given,and show the validity of the theoretical results by numerical simulations.