Asymptotic stability problem of predator–prey system with linear diffusion

Abstract

As the primary killer of health, the class of infectious diseases is the greatest threat to humanity. At present, international methods of studying the large-scale spatial transmission of sudden infectious diseases from the perspective of dynamics can be divided into two categories. On the one hand, top international biomedical and medical teams discuss the restraining effects of some prevention and control strategies on infectious diseases, such as smallpox, malaria, hand, foot and mouth disease and pandemic influenza, from the perspective of pragmatism. On the other hand, researchers in theoretical physics and network science tend to use compound population network models to explore the internal dynamic mechanism of spatial transmission of infectious diseases. This paper establishes a Lotka–Volterra dispersal predator–prey system in a patchy environment. It shows the existence of model boundary equilibria and asymptotic stability under an appropriate condition. This paper adopts the method of global Lyapunov function and the results of graph theory. We also consider a predator–prey dynamical model in a patchy environment, where the prey and predator individuals in each compartment can travel among n patches.

Integrated Stochastic Investigation of Singularly Perturbed Delay Differential Equations for the Neuronal Variability Model

“…Sometimes, there is no solution to unperturbed problems in singularly perturbed theory. Te solution whose function ε may stop existing when ε � 0, but when a solution to the unperturbed problem does exist, its numerical features vary from the real result for arbitrarily little nonzero ε [5][6][7]. In these cases, the solution ε � 0 is essentially distinct in quality from the corresponding solutions attained in the boundary ε ⟶ 0.…”