This paper deals with a Keller–Segel type parabolic–elliptic system involving nonlinear diffusion and chemotaxis in smoothly bounded domain , under no-flux boundary conditions. The contains Fokker–Planck motility function .

We study a two‐dimensional chemotaxis‐fluid system in bounded convex domain with smooth boundary under no‐flux conditions for bacterial density and oxygen concentration no‐slip condition fluid velocity. A global existence result of classical solutions is established large initial data possibly singular chemotactic sensitivity super‐linear consumption rate.

This paper studies a reaction–advection–diffusion prey–predator system in one spatial dimension. Adapting the Lotka–Volterra-type functional response, we prove global existence and boundedness of solutions bounded open interval. In view asymptotic behavior solutions, show that if predation is weak, semi-trivial steady state at which prey only survive globally asymptotically stable. case strong predation, positive stable when predator-taxis weak.

<abstract> <p>This paper studies a reaction-diffusion-advection system describing directed movement of immune cells toward chemokines during the process. We investigate global solvability model based on bootstrap argument for minimal chemotaxis models. also examine stability nonconstant steady states and existence periodic orbits from theoretical aspects bifurcation analysis. Through numerical simulations, we observe occurrence or time-periodic pattern formations.</p>...

Advection and cross-diffusion terms are obtained as dispersal strategies of biological species. The focus the paper is their connection to a given population dynamics. In particular, meaningful parameter regimes obtained. Eventually, we obtain systematic approach construct an advection or term from dynamics find cross-diffusion.

Biological organisms leave their habitat when the environment becomes harsh. The essence of a biological dispersal is not in rate, but capability to adjust environmental changes. In nature, conditional asymmetric strategies appear due spatial and temporal heterogeneity environment. Authors show that such strategy evolutionary selected context two-patch problem Lotka-Volterra competition model. They conclude that, if taken, necessarily disadvantageous even for case there no fluctuation at all.

In this paper, we propose a food chain model in which the primary predator moves directly toward areas of high prey density. Simultaneously, predator, serves as for secondary indirectly influences directional movements through cues such chemical signals, scents, or excretions. We investigate whether distinct direct taxis and indirect taxis, observed prey–predator dynamics, are also manifested proposed model. Our study demonstrates that model, incorporates both prey‐taxis, possesses bounded...