Pattern formation by the global limits of a nonlinear competitive interaction in n dimensions.

Abstract

This paper describes a class of nonlinear systems that include processes of pattern formation, short term memory, interpopulation competition, and parallel processing. These systems show how continuously fluctuating data patterns can be processed by noisy populations having finitely many excitable sites. Particular examples are found in vertebrate retina and sensory cortex, as well as certain nonneural developing tissues. After an initial period of seemingly random behavior, that is described by a finite series of iterated decisions or enhancement steps, a global consensus or asymptotic pattern is reached. This is true given any number of competing populations, any mean competition function, and any number of random factors determining interpopulation signals. Which pattern will be chosen can depend on initial data and system structure in a complicated fashion. The results demonstrate a robust design that joins together the dynamics of mass action, the geometry of interpopulation competition, and the statistics of signal generation.