Patterns, fronts, and localized structures of a prototypical model for population dynamics interaction are studied. The physical content of the model is the coexistence of a simple random walk for the motion of the individuals with a nonlinearity in the competitive struggle for resources which simultaneously stresses the Allee effect and interaction at a distance. Mathematically, the model is variational and exhibits coexistence between different stable extended states. Solutions are obtained, the phase diagram is constructed, and the emergence of localized structures is investigated.
|Original language||American English|
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|State||Published - 1 Nov 2005|