This paper deals with a three-species predator-prey system prey-taxis \begin{document}$ \begin{eqnarray*} \left\{ \begin{split}{} &u_t = d_{1}\Delta u-\chi_{1}\nabla\cdot(u\nabla w)+\gamma_{1}uw-\theta_{1}u-\beta_{1}uv,&(x,t)\in \Omega\times (0,\infty),\\ &v_t d_{2}\Delta v-\chi_{2}\nabla\cdot(v\nabla w)+\gamma_{2}vw-\theta_{2}v-\beta_{2}uv,&(x,t)\in &w_t d_{3}\Delta w-(u+v)...

Current theory suggests that many signaling systems evolved from preexisting cues. In aposematic systems, prey warning signals benefit both predator and prey. When the signal is highly beneficial, a third species often evolves to mimic the toxic species, exploiting the signaling system for its own protection. We investigated the evolutionary dynamics of predator cue utilization and prey signali...

We are interested in the impact of natural selection in a prey-predator community. We introduce an individual-based model of the community that takes into account both prey and predator phenotypes. Our aim is to understand the phenotypic coevolution of prey and predators. The community evolves as a multi-type birth and death process with mutations. We first consider the infinite particle approx...

In this article, we study a diffusive predator-prey system with prey-taxis under homogeneous Neumann boundary conditions. We establish the existence and boundedness of nonnegative global solutions. Through comparison without prey-taxis, find that positive constant equilibrium remains stable for while negative makes it unstable.

<p style='text-indent:20px;'>The change of behaviors prey in the form vigilance significantly affects dynamics a predator-prey system. In this paper, we consider discrete-time model, where acts as trade-off between safety and growth rate prey. Mathematical properties such stability, permanence, both flip Neimark-Sacker bifurcations model are investigated. Numerical simulations carried out...

Two recent articles by Geisler and Diehl use Bayesian statistical decision theory to model the co-evolution of predator and prey in a simple, game-like environment. The prey is characterized by its coloration. The predator is characterized by the chromatic sensitivity of its visual system and its willingness to attack. The authors demonstrate how the coloration of prey and the perceptual system...