Pattern Formation in a Nonlocal Fisher–Kolmogorov–Petrovsky–Piskunov Model and in a Nonlocal Model of the Kinetics of an Metal Vapor Active Medium.

Nonlocal versions of the reaction-diffusion type population equations can describe the evolution of spatiotemporal structures (patterns) depending on the equation parameter domain. Under conditions of weak diffusion, numerical methods have been used to compare the processes of spatiotemporal pattern formation in a nonlocal population model described by a one-dimensional generalized Fisher–Kolmogorov–Petrovsky–Piskunov equation with nonlocal competitive losses and in a two-dimensional nonlocal version of the kinetic model of quasi-neutral plasma of metal vapor active media described by the kinetic equation with nonlocal cubic nonlinearity. The effect of relaxation on the pattern formation is studied. [ABSTRACT FROM AUTHOR]