Biological Competition: Decision Rules, Pattern Formation, and Oscillations
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This article summarizes some of the new mathematical and physical ideas about competition that have emerged during the past eight years. Each of these ideas can be expressed in several ways. For example, every competitive system induces a decision scheme that can be used to analyze its global dynamics. Otherwise expressed, you learn a lot about a competition by keeping track of who is winning it! Otherwise expressed again, you can understand more about certain nonequilibrium systems by measuring where they change fastest rather than where they achieve equilibrium. Still otherwise expressed, you can sometimes learn a lot about a continuous parallel process by embedding a discrete serial process into it, even though you couldn’t guess which serial process to embed without referring to the parallel process.
KeywordsEquilibrium Point Pattern Formation Decision Scheme Decision Boundary Sustained Oscillation
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- 1.Darwin, C. (1859) On the Origin of Species (London).Google Scholar
- 3.Grossberg, S. (1973) Stud. Appl. Math. 52, 217–257.Google Scholar
- 5.Grossberg, S. (1978) in Progress in Theoretical Biology, eds. Rosen, R. & Snell, F. ( Academic, New York ), pp. 183–232.Google Scholar
- 12.Grossberg, S. (1978) in Progress in Theoretical Biology, eds. Rosen, R. & Snell, F. ( Academic, New York ), pp. 233–374.Google Scholar
- 13.Leibniz, G. W. (1925) The Monadology and Other Philosophical Writings, translated by Latta, R. (Oxford Univ. Press, London).Google Scholar
- 14.Hodgkin, A. L. (1964) The Conduction of the Nervous Impulse (Thomas, Springfield, IL).Google Scholar
- 15.Katz, B. (1966) Nerve, Muscle, and Synapse ( McGraw-Hill, New York).Google Scholar
- 22.Grossberg, S. (1980) Bull. Math. Biol., in press.Google Scholar