# Non-classical relaxation cycle of a three-dimensional system of Lotka-Volterra equations

## Abstract

A mathematical model of the well-known Belousov's reaction is the object of study. It is reasonable to assume that one coefficient in the corresponding system of differential equations is large, while the other parameters are finite. Non-standard tools taking account of the peculiarities of the problem bring one to a theorem on the existence of a relaxation cycle, allowing at the same time to reveal its characteristic features.

- Authors:

- P.G. Demidov Yaroslavl State University, Yaroslavl (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21202920

- Resource Type:
- Journal Article

- Journal Name:
- Sbornik. Mathematics

- Additional Journal Information:
- Journal Volume: 191; Journal Issue: 4; Other Information: DOI: 10.1070/SM2000v191n04ABEH000472; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; RELAXATION; THREE-DIMENSIONAL CALCULATIONS; VOLTERRA INTEGRAL EQUATIONS

### Citation Formats

```
Kolesov, Yu S.
```*Non-classical relaxation cycle of a three-dimensional system of Lotka-Volterra equations*. United States: N. p., 2000.
Web. doi:10.1070/SM2000V191N04ABEH000472; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Kolesov, Yu S.
```*Non-classical relaxation cycle of a three-dimensional system of Lotka-Volterra equations*. United States. doi:10.1070/SM2000V191N04ABEH000472; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Kolesov, Yu S. Sun .
"Non-classical relaxation cycle of a three-dimensional system of Lotka-Volterra equations". United States. doi:10.1070/SM2000V191N04ABEH000472; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
```

```
@article{osti_21202920,
```

title = {Non-classical relaxation cycle of a three-dimensional system of Lotka-Volterra equations},

author = {Kolesov, Yu S},

abstractNote = {A mathematical model of the well-known Belousov's reaction is the object of study. It is reasonable to assume that one coefficient in the corresponding system of differential equations is large, while the other parameters are finite. Non-standard tools taking account of the peculiarities of the problem bring one to a theorem on the existence of a relaxation cycle, allowing at the same time to reveal its characteristic features.},

doi = {10.1070/SM2000V191N04ABEH000472; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},

journal = {Sbornik. Mathematics},

issn = {1064-5616},

number = 4,

volume = 191,

place = {United States},

year = {2000},

month = {4}

}

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