On Persistence and Stability of Some Spatially Inhomogeneous Systems

Local and global stability and persistence of some coupled map lattices (CMLs) and partial differential equations are studied. A logistic CML with noninteger time step and delay is introduced. The persistence results for reaction–diffusion equations are extendable to the telegraph reaction–diffusion equation for a sufficiently small delay parameter. The stability and persistence results are applied to ecology, physics, economics, and immunology