The classical macroscopic chemotaxis equations have previously been derived from an individual-based description of the tactic response of cells that use a "run-and-tumble" strategy in response to environmental cues [17,18]. Here we derive macroscopic equations for the more complex type of behavioral response characteristic of crawling cells, which detect a signal, extract directional informati...

This article deals with a 2 ? reaction-diffusion-taxis model consisting of Michaelis-Menten functional response predator-prey system. The critical section this is that temporal-spatial evolution the predators? velocity depends largely on gradient prey. But beyond that, system also inscribes prey-taxis mechanism an immediate movement predator u in to change prey v (which leads collection u). By ...

Abstract Multi-taxis appears in society interactions and cancer treatment. Society can lead to the complex dynamical behavior biology even criminology ([43, 65, 190]).

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.

Abstract This article is concerned with the stationary problem for a prey-predator model prey-taxis/predator-taxis under homogeneous Dirichlet boundary conditions, where interaction governed by Beddington-DeAngelis functional response. We make detailed description of global bifurcation structure coexistence states and find ranges parameters which there exist states. At same time, some sufficien...