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Author(s): Grossberg, S. |
Year: 1978
Citation: Journal of Mathematical Analysis and Applications, 66, 470-493
Abstract: The following problem, in one form or another, has intrigued philosophers and scientists for hundreds of years: How do arbitrarily many individuals, populations, or states, each obeying unique and personal laws, ever succeed in harmoniously interacting with each other to form some sort of stable society, or collective mode of behavior? Otherwise expressed, if each individual obeys complex laws, and is ignorant of other individuals except via locally received signals, how is social chaos averted ? How can local ignorance and global order, or consensus, be reconciled? This paper considers' a class of systems in which this dilemma is overcome.
We begin by asking what design constraints must be imposed on a system of competing populations in order that it be able to generate a global limiting pattern, or decision, in response to arbitrary initial data ? This paper proves that global pattern formation occurs in systems of the form
Topics:
Biological Learning,
Models:
Other,
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