1990 Fiscal Year Final Research Report Summary
Mathematical Study on the Stability and Organization of Biological System
| Project/Area Number |
01540546
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
生態学
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| Research Institution | Kyoto University |
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Principal Investigator |
NAKANO Shigesada Kyoto University, Dept. Biophysics Research Associate, 理学部, 助手 (70025443)
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| Co-Investigator(Kenkyū-buntansha) |
KOBUCHI Youichi Ryukoku Univ. Dept. Electronics & Informatics, 理工学部, 教授 (60025450)
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| Project Period (FY) |
1989 – 1990
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| Keywords | Competition Community / Community Structure / Coral Reef Community / Succession / Logic Networks / Lyapunov Function / Neural Networks / Cell Interaction |
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| Research Abstract |
Eco-systems, biological community, neural networks and the like are modeled as systems consisting of interacting populations. We investigated the behavior of such interacting systems from the standpoint of their stable pattern generation capability and interaction strength, and discovered the following specific features :
1. A Lotka-Volterra system for a multiple competing species community was analyzed to illustrate how community structure is reorganized upon invasion of new species. By analyzing the stability property of equilibrium states, we obtained a criterion for invasion of a new species, which explains directional changes of some quantities characteristic to successional processes. We further investigated the effect of invading predators on the community structure, in terms of predator-mediated coexistence and predator-induced instability.
2. Community structures of Hermatypic Corals was studied from view points of zonation, coverage and ecological succession. Particularly the temporal change of species diversity was explained by introducing a dynamical model.
3. For a network of binary state elements, we first characterized the existence of state functions through the properties on their difference functions. Then a state function is a Lyapunov function for some network if the function value decreases as the system undergoes state changes. We applied the result for networks of McCulloch-Pitts type model neurons and found, in its simplest linear analysis, that a network has a Lyapunov function if the weight matrix is quasi-symmetric. For more general logic net, we also showed that a certain type of symmetry for each pair of elements is sufficient for the existence of Lyapunov functions.
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