| Title:
|
Дифференциальные уравнения динамики биологических сообществ (Russian) |
| Title:
|
Differential equations of the dynamics of biological communities (English) |
| Title:
|
Differentialgleichungen für die Dynamik biologischer Gemeinschaften (German) |
| Author:
|
Gil'derman, Yu. I. |
| Language:
|
Russian |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
21 |
| Issue:
|
3 |
| Year:
|
1976 |
| Pages:
|
185-212 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. () |
| MSC:
|
34D10 |
| MSC:
|
60J99 |
| MSC:
|
92A15 |
| MSC:
|
92D10 |
| MSC:
|
92D25 |
| idZBL:
|
Zbl 0337.92012 |
| idMR:
|
MR0411692 |
| DOI:
|
10.21136/AM.1976.103638 |
| . |
| Date available:
|
2008-05-20T18:04:44Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103638 |
| . |
| Reference:
|
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| . |
