Geodesic
Дифференциальные уравнения динамики биологических сообществ
Applications of Mathematics, Tome 21 (1976) no. 3, pp. 185-212

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The paper contains a survey of models for development of biological societies. Only deterministic models of sufficiently large societies are considered, which permits to apply differential and integro-differential equations and to take into account interrelations of the type of competition, symbiosis, parasitism, "beast of prey-prey", etc. From the vast literature on this topic, including some applications, the author discusses mainly those works which initiated new directions of investigation and which describe the principal ideas. The works used for this survey are connected by their mathematical ideas, namely by the qualitative study of the model systems of differential equations. The existence of stationary points, their location, stability and character, boundedness or periodicity of solutions, a general phase picture of the system under investigation - the answers to these questions yield also answers to biological problems.
The paper contains a survey of models for development of biological societies. Only deterministic models of sufficiently large societies are considered, which permits to apply differential and integro-differential equations and to take into account interrelations of the type of competition, symbiosis, parasitism, "beast of prey-prey", etc. From the vast literature on this topic, including some applications, the author discusses mainly those works which initiated new directions of investigation and which describe the principal ideas. The works used for this survey are connected by their mathematical ideas, namely by the qualitative study of the model systems of differential equations. The existence of stationary points, their location, stability and character, boundedness or periodicity of solutions, a general phase picture of the system under investigation - the answers to these questions yield also answers to biological problems.
DOI : 10.21136/AM.1976.103638
Classification : 34D10, 60J99, 92A15, 92D10, 92D25 
Gil'derman, Yu. I. Дифференциальные уравнения динамики биологических сообществ. Applications of Mathematics, Tome 21 (1976) no. 3, pp. 185-212. doi: 10.21136/AM.1976.103638
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