Asymptotic stability problem of predator–prey system with linear diffusion
- Autores: Wanqiu Li, Hailong Dao, Chang Sun, Ali Sedki
- Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 8, Nº. 1, 2023, págs. 15-26
- Idioma: inglés
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Resumen
As the primary killer of health, the class of infectious diseases is the greatest threat to humanity. At present, internationalmethods of studying the large-scale spatial transmission of sudden infectious diseases from the perspective of dynamicscan be divided into two categories. On the one hand, top international biomedical and medical teams discuss the restrainingeffects of some prevention and control strategies on infectious diseases, such as smallpox, malaria, hand, foot and mouthdisease and pandemic influenza, from the perspective of pragmatism. On the other hand, researchers in theoretical physicsand network science tend to use compound population network models to explore the internal dynamic mechanism ofspatial transmission of infectious diseases. This paper establishes a Lotka–Volterra dispersal predator–prey system in apatchy environment. It shows the existence of model boundary equilibria and asymptotic stability under an appropriatecondition. This paper adopts the method of global Lyapunov function and the results of graph theory. We also considera predator–prey dynamical model in a patchy environment, where the prey and predator individuals in each compartmentcan travel amongnpatches
