Stability of solutions of chemotaxis equations in reinforced random walks

In this paper we consider a nonlinear system of differential equations consisting of one parabolic equation and one ordinary differential equation. The system arises in chemotaxis, a process whereby living organisms respond to chemical substance by moving toward higher, or lower, concentrations of the chemical substance, or by aggregating or dispersing. We prove that stationary solutions of the system are asymptotically stable.  2002 Elsevier Science (USA). All rights reserved.