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

For citation:

Kurushina S. E., Maksimov V. V. Noise-­induced phase transitions in competition processes in the external fluctuated media. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 1, pp. 88-100. DOI: 10.18500/0869-6632-2010-18-1-88-100

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
519.6
DOI: 
10.18500/0869-6632-2010-18-1-88-100

Noise-­induced phase transitions in competition processes in the external fluctuated media

Autors: 
Kurushina Svetlana Evgenevna, Samara State University
Maksimov Valerij Vladimirovich, Samara National Research University
Abstract: 

The influence of external additive homogeneous isotropic field of Gauss fluctuations to evolution of competition processes, which described by Lotka–Volterra equations, where taking into account the mobility of weak population individuals and spatial and temporal fluctuations of resource, has been researched. The numerical simulation of considered model was performed. It was shown that considered system have three different types of stationary solutions: classical solution, which corresponds to extinction of weak population; solution, which similar to phenomenon of kinetic transition, called «occupation of environment»; and a new type of solutions, which correspond to stationary state, where average in volume and asymptotic in time density of population size of weak species more than corresponding density of population size of strong species. Parametric diagrams for different types of solutions were plotted. Average in volume and asymptotic in time density of population size of weak and strong species dependences from main parameters were investigated. 

Key words: 
Noise-induced phase transitions
competition processes
numerical simulation
parametric diagram
Reference: 
  1. Horsthemke W, Lefever R. Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology. Moscow: Mir; 1987. 399 p. (in Russian).
  2. Svirezhev YuM. Nonlinear Waves, Dissipative Structures, and Catastrophes in Ecology. Moscow: Nauka; 1987. (in Russian).
  3. Benilov ES, Pelinovskii EN. Dispersionless wave propagation in nonlinear fluctuating media. JETP. 1988;67(1):98–103.
  4. Moiseev SS, Petviashvily VI, Toor AV, Yanovsky VV. The influence of compressibility on the selfsimilar spectrum of subsonic turbulence. Physica D: Nonlinear Phenomena. 1981;2(1):218–223. DOI: 10.1016/0167-2789(81)90075-0.
  5. Zavershinskii IP, Kogan EYa. The attenuation of shock waves in a nonequilibrium gas. High Temperature. 2000;38(2):273–277.
  6. Klyatskin VI. Stochastic Equations and Waves in Randomly-Inhomogeneous Media. Moscow: Nauka; 1980. (in Russian).
  7. Mikhailov AS, Uporov IV. Critical phenomena in media with breeding, decay, and diffusion. Phys. Usp. 1984;27(9):695–714.
  8. Autowave Processes in Systems with Diffusion. Ed. Grekhova MT. Gorky: Acad. Sei. USSR; 1981. (in Russian).
  9. Anishchenko VS, Vadivasova TE, Astakhov VV. Nonlinear dynamics of chaotic and stochastic systems. Fundamental principles and selected issues. Saratov: Saratov Univ. Publ.; 1999. 368 p. (in Russian).
  10. Haken G. Synergetics. Moscow: Mir; 1980. (in Russian).
  11. Volterra V. Mathematical Theory of the Struggle for Existence. Moscow: Mir; 1976. (in Russian).
  12. Svirezhev YuM, Logofet DO. Stability of Biological Communities. Moscow: Nauka, Fizmatlit; 1978. 352 p. (in Russian).
  13. Gause GF. The struggle for existence. Moscow; Izhevsk: Regular and chaotic dynamics; 2000. 234 p. (in Russian).
  14. Mikhailov AS, Uporov IV.Noise-induced phase transition and the percolation problem for fluctuating media with diffusion. JETP. 1980;52(5):989–996.
  15. Vostokin SV, Kurushina SE. Modeling of competition process in noisy medium on cluster-based computing systems. Izvestia of the Samara Scientific Center of the Russian Academy of Sciences. 2005;7(1):143–148 (in Russian).
  16. Yaroshchuk IO, Gulin OE. Statistical modeling method for hydroacoustic problems. Vladivostok: Dalnauka; 2002. 352 p.
  17. Ivanov MF, Shvets VF. A stochastic differential equation method for calculating the kinetics of a plasma with collision. U.S.S.R. Comput. Math. Math. Phys. 1980;20(3):146–155.
  18. Kholodniok M, Klich A, Kubichek M, Marek M. Methods for Analysis of Nonlinear Dynamic Models. Moscow: Mir; 1991. 368 p. (in Russian).
  19. Akhmanov SA, Dyakov YuE, Chirkin AS. Introduction to Statistical Radiophysics and Optics. Moscow: Nauka, Fizmatlit; 1981. 640 p. (in Russian).
  20. Bakalov VP. Digital simulation of random processes. Moscow: SAYNS-PRESS; 2002. 88 p. (in Russian).
  21. Kurushina SE, Levchenko LV, Maximov VV. Mathematical modeling of the competition process in the resource-consumer system in a fluctuating environment. Obozrenie prikladnoy i promishlennoy matematitki. 2006;13(4):660–661 (in Russian).
  22. Prokhorov SA, Lezin IA, et al. Automated system of approximative analysis of distribution laws by orthogonal polynomials and neural network functions. Samara: Samara science centre of the RAS; 2007. 528 p. (in Russian).
  23. Neimark YuI, Kogan NYa, Saveliev VP. Dynamic models of management theory. Moscow:  Nauka; 1985. 400 p. (in Russian)
  24. Gamma E, Helm R, Johnson R, Vlissides J. Object Oriented Design Techniques. Design patterns. St. Petersburg: Piter; 2003. 368 p. (in Russian)
Received: 
01.12.2008
Accepted: 
02.04.2009
Published: 
31.03.2010
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