Historically, infectious diseases caused considerable damage to human societies, and they
continue to do so today. To help reduce their impact, mathematical models of disease …

Climate change has become increasingly severe, threatening ecosystem stability and, in
particular, biodiversity. As a typical indicator of ecosystem evolution, vegetation growth is …

We investigate the complex behavior and chaos control in a discrete-time prey-predator
model. Taking into account the Leslie-Gower prey-predator model, we propose a discrete …

Infectious diseases are a threat to human health and a hindrance to societal development.
Consequently, the spread of diseases in both time and space has been widely studied …

Allee effect that refers to a positive relationship between individual fitness and population
density provides an important conceptual framework in conservation biology. While …

Synapse coupling can benefit signal exchange between neurons and information encoding
for neurons, and the collective behaviors such as synchronization and pattern selection in …

It is well known that vegetation patterns characterize the distribution of the vegetation and
provide some signs for vegetation protection. The positive feedbacks regulation between the …

Pattern estimation and selection in media can give important clues to understand the
collective response to external stimulus by detecting the observable variables. Both reaction …

The popularity of the Web improves the growth of web threats. Formulating mathematical
models for accurate prediction of malicious propagation over networks is of great …

In this paper, we consider a predator–prey model with herd behavior and cross-diffusion
subject to homogeneous Neumann boundary condition. Firstly, the existence and priori …