ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Muzychuk O. V. Probability characteristics of «beast-sacrifice» system with random fluctuations of parameters. Izvestiya VUZ. Applied Nonlinear Dynamics, 1997, vol. 5, iss. 2, pp. 80-86. DOI: 10.18500/0869-6632-1997-5-2-80-86

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 1997no2-3p080.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
538.56:519.25
DOI: 
10.18500/0869-6632-1997-5-2-80-86

Probability characteristics of «beast-sacrifice» system with random fluctuations of parameters

Autors: 
Muzychuk Oleg Vladimirovich, Nizhny Novgorod State University of Architecture
Abstract: 

Well-known Lottky — Volterra scheme for self-regulated «beast—sacrifice» associations with random fluctuations of habitat conditions was considered. Fluctuationsof parameters werc supposed аs the Gaussian delta—correlated stochastic processes. Stationary mean—square characteristics of populations numbers were obtained The situation was considered in more detail when only trophical coefficient fluctuations of «sacrifices» take place. Stationary probability densities of populations numbers were investigated. Closed equations described relaxation of mean values and dispersions were obtained and solved by computer. It was obtained in particular, that when fluctuations of the trophical cocfficient are too intensive, the system enters thecritical regime, when maximums of probability densitics move to zero. That time the relaxation scales for mean values and dispersions increase and the process of relaxation proceeds with essential oscillations.

Key words: 
-
Acknowledgments: 
The work was carried out with the support of the State Committee of the Russian Federation for Higher Education (grant 95-0-8.3-36).
Reference: 
  1. Rabinovich MI, Trubetskov DI. Introduction to the Theory of Oscillations and Waves. M.: Nauka; 1984. 431 p. (in Russian).
  2. Svirezhev YuM, Logofet DО. Sustainability of biological communities. M.: Nauka; 1978. 352 p. (in Russian).
  3. Svirezhev YuM. Nonlinear Waves, Dissipative Structures and Catastrophes in Ecology. М.: Nauka; 1987. 365 p.(in Russian).
  4. Dimentber МF. Precise solutions of the Fokker-Planck-Kolmogorov equation for some multidimensional dynamical systems. J. Appl. Math. Mech. 1983;47(4):555-558.
  5. Muzychuk OV. Some accurate results for the probabilistic characteristics of the stochastic Verhulst equation. Izvestiya VUZ. Applied Nonlinear Dynamics. 1996;4(3):18-24. (in Russian).
  6. Muzychuk OV. Non-stationary probabilistic characteristics of the stochastic Ferhulst equation. Izvestiya VUZ. Applied Nonlinear Dynamics. 1996;4(3):25-30. (in Russian).
  7. Malakhov АN. Cumulative analysis of non-Gaussian random processes and their transformations. М.: Sovetskoe Radio; 1978. 375 p. (in Russian).
Received: 
19.03.1997
Accepted: 
06.06.1997
Published: 
17.07.1997
  • 134 reads