Waves in a Hyperbolic Predator–Prey System

We address a hyperbolic predator–prey model, which we formulate with the use of Cattaneo model for chemosensitive movement. put special focus on case when equation flux species takes form conservation law—that is, assume relation between diffusivity and sensitivity coefficients. Regarding this relation, there are pieces arguing its relevance to some real-life populations, e.g., copepods (Harpacticoida), in biological literature (see reference list). Thanks mentioned conservatism, get exact solutions describing travelling shock waves limited cases. Next, employ numerical analysis continuing these wider parametric domain. As result, discover smooth solitary waves, turn out be quite sustainable small moderate initial perturbations. Nevertheless, perturbations cause shedding predators from main core wave, can treated as settling mechanism. Besides, localized make colliding demonstrating peculiar quasi-soliton phenomena sometimes resembling leapfrog playing. An interesting side result is onset migration due explosion overpopulated cores.