Infinite dimensional relaxation oscillation in aggregation-growth systems
A three-component diffusion-growth system with two-mode dispersion and a two-component cross-diffusion system are introduced. These models are motivated by pheromone-driven aggregation. The cross-diffusion model is derived as a formal limit of the diffusion-growth model. For both models bifurcation diagrams are obtained for decreasing intrinsic growth rates \(\delta\). In particular, for small \(\delta\) oscillatory solutions emerge. If \(\delta\) is sufficiently small, the existence of infinite-dimensional relaxation-oscillation consisting of fast and slow dynamics is proved under appropriate assumptions.
scientific article; zbMATH DE number 6081726