Abstract
Competition solves a universal problem about pattern processing by cellular systems. Competition allows cells to automatically retune their sensitivity to avoid noise and saturation effects. All competitive systems induce decision schemes that permit them to be classified. Systems are identified that achieve global pattern formation, or decision-making, no matter how their parameters are chosen. Oscillations can occur due to contradictions in a system's decision scheme. The pattern formation and oscillation results are extreme examples of a complementarity principle that seems to hold for competitive systems. Nonlinear competitive systems can sometimes appear, to a macroscopic observer, to have linear and cooperative properties, although the two types of systems are not equivalent. This observation is relevant to theories about the evolutionary transition from competitive to cooperative behavior.
Keywords: development, cooperation, voting paradox, Volterra-Lotka, self-organization
Full text
PDF
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Grossberg S. Decisions, patterns, and oscillations in nonlinear competitive systems with applications to Volterra-Lotka systems. J Theor Biol. 1978 Jul 6;73(1):101–130. doi: 10.1016/0022-5193(78)90182-0. [DOI] [PubMed] [Google Scholar]
- Grossberg S. Do all neural models really look alike? A comment on Anderson, Silverstein, Ritz, and Jones. Psychol Rev. 1978 Nov;85(6):592–596. [PubMed] [Google Scholar]
- Grossberg S. How does a brain build a cognitive code? Psychol Rev. 1980 Jan;87(1):1–51. doi: 10.1007/978-94-009-7758-7_1. [DOI] [PubMed] [Google Scholar]
- Grossberg S., Levine D. Some developmental and attentional biases in the contrast enhancement and short term memory of recurrent neural networks. J Theor Biol. 1975 Sep;53(2):341–380. doi: 10.1016/s0022-5193(75)80009-9. [DOI] [PubMed] [Google Scholar]
- Grossberg S. Neural pattern discrimination. J Theor Biol. 1970 May;27(2):291–337. doi: 10.1016/0022-5193(70)90143-8. [DOI] [PubMed] [Google Scholar]
- Grossberg S. Pattern formation by the global limits of a nonlinear competitive interaction in n dimensions. J Math Biol. 1977 Jul 19;4(3):237–256. doi: 10.1007/BF00280974. [DOI] [PubMed] [Google Scholar]
- Kauffman S. A., Shymko R. M., Trabert K. Control of sequential compartment formation in Drosophila. Science. 1978 Jan 20;199(4326):259–270. doi: 10.1126/science.413193. [DOI] [PubMed] [Google Scholar]
- Levine D. S., Grossberg S. Visual illusions in neural networks: line neutralization, tilt after effect, and angle expansion. J Theor Biol. 1976 Sep 21;61(2):477–504. doi: 10.1016/0022-5193(76)90031-x. [DOI] [PubMed] [Google Scholar]
- Mimura M., Murray J. D. On a diffusive prey--predator model which exhibits patchiness. J Theor Biol. 1978 Dec 7;75(3):249–262. doi: 10.1016/0022-5193(78)90332-6. [DOI] [PubMed] [Google Scholar]
- Smale S. On the differential equations of species in competition. J Math Biol. 1976 Apr 29;3(1):5–7. doi: 10.1007/BF00307854. [DOI] [PubMed] [Google Scholar]