Existence and dimensional lower bound for the global attractor of a PDE model for ant trail formation

Abstract: We study the asymptotic behavior of a nonlinear PDE model for ant trail formation, which was introduced in [3]. We establish the existence of a compact global attractor and prove the nonlinear instability of the homogeneous steady state under an inviscid instability condition. We also provide a dimensional lower bound on the attractor. Alternatively, we prove that if the interaction parameter is sufficiently small, the homogeneous steady state is globally asymptotically stable.