Spreading speeds and linear determinacy of time dependent diffusive cooperative/competitive systems
This is a study of spreading speeds and linear determinacy of diffusive either cooperative or competitive systems of the form \(u_t(t,x)=(Au)(t,x)+F(t,u(t,x))\) either in \({\mathbb R}^N\) or on the lattice \({\mathbb Z}^N\). Here \(A\) is a random or nonlocal dispersal operator, or a discrete dispersal operator. The nonlinearity \(F(t, u)\) is cooperative or competitive in \(u\) and is recurrent in time, e.g. \(F(t u)\) periodic and almost periodic in \(t\) as special cases. The notion of spreading speed intervals for diffusive cooperative systems is introduced via the natural features of spreading speeds. Then, some principal Lyapunov exponent and principal Floquet bundle theory for linear cooperative systems of ordinary differential equations is developed. These are the tools used in the proof that a diffusive cooperative system has a single spreading speed and is linearly determinant. Finally, by transforming a diffusive competitive system to a diffusive cooperative system and applying previous results, upper and lower bounds for the spreading speed intervals for diffusive competitive systems are obtained.
scientific article; zbMATH DE number 6890651
scientific article