The study of spatio-temporal behaviour of ecological systems is fundamentally important as
it can provide deep understanding of species interaction and predict the effects of …

In this paper, we investigate the phenomena of pattern formation for a predator–prey model
with herd behavior and cross-diffusion. We give the conditions for cross-diffusion induced …

There are random and directed movements of predator and prey populations in many
natural systems which are strongly influenced and modified by spatial factors. To investigate …

In this paper, we consider a predator-prey model with herd behavior and hyperbolic mortality
subject to the homogeneous Neumann boundary condition. Firstly, we prove the existence …

Competitive behavior, like predation, widely exists in the world which has influences on the
dynamics of ecosystems. Though a good knowledge for the patten formation and selection …

In this paper, we propose a predator–prey model with herd behavior and prey-taxis. Then,
we analyze the stability and bifurcation of the positive equilibrium of the model subject to the …

Spatiotemporal dynamics in a ratio-dependent predator–prey model with diffusion is studied
by analytical methods. Normal forms associated with codimension-two Hopf–Turing …

In this paper, a ratio-dependent predator–prey model with diffusion is considered. The
stability of the positive constant equilibrium, Turing instability, and the existence of Hopf and …

Prey-predator interaction is one of the most commonly observed relationships in ecosystem.
In the study of prey-predator models, it is frequently assumed that the changes in population …

The present investigation deals with the necessary conditions for Turing instability with zero-
flux boundary conditions that arise in a ratio-dependent predator–prey model involving the …