Coloured-noise-induced transitions in nonlinear structures

• Autorzy: Mankin R. , Laas T. , Soika E. , Sauga A. , Rekker A. , Ainsaar A. , Ugaste U.
• Języki publikacji: EN

Abstrakty

EN

In a stochastic framework, macroscopic approaches are sought to describe microscopic interaction between different species. Coloured-noise-induced transitions in stochastic N-species Lotka-Volterra systems are considered analytically as an appropriate model extendable to many natural and nano-technological processes. All the results discussed are computed by means of a dynamical mean-field approximation. It is demonstrated that interplay of coloured noise and interaction intensities of species can generate a variety of cooperation effects, such as discontinuous transitions of the mean population density, noise-induced Hopf bifurcations and relaxation oscillation. The necessary conditions for the cooperation effects are also discussed. Particularly, it is established that, in the case of the Beddington functional response, in certain parameter regions of the model an increase in noise correlation time can cause multiple transitions (more than two) between relaxation oscillatory regimes and equilibrium states.

Słowa kluczowe

EN

non-equilibrium fluctuations; coloured-noise-induced transitions; mean-field approximation; Hopf bifurcation; stochastic Lotka-Volterra system

• Wydawca: Institute of Nuclear Chemistry and Technology
• Czasopismo: Nukleonika
• Rocznik: 2008
• Tom: Vol. 53, No. 3
• Strony: 127--134
• Opis fizyczny: Bibliogr. 27 poz., rys.

Twórcy

autor

Mankin R.

autor

Laas T.

autor

Soika E.

autor

Sauga A.

autor

Rekker A.

autor

Ainsaar A.

autor

Ugaste U.

• Tallinn University, 25 Narva Road, 10120 Tallinn, Estonia, Tel.: [phone], Fax: [phone],

Bibliografia

• 1 Arditi R, Ginzburg LR (1989) Coupling in consumerresource dynamics: ratio-dependence. J Theoret Biol 139:311–326
• 2. Astrov YuA, Fradkov AL, Guzenko PYu (2008) Control of a noise-induced transition in a nonlinear dynamical system. Phys Rev E 77:026201
• 3. Astrov YuA, Logvin YuA (1997) Formation of clusters of localized states in a gas discharge system via a selfcompletion scenario. Phys Rev Lett 79:2983–2986
• 4. Beddington JR (1975) Mutual interference between parasites or predators and its effect on searching efficiency. J Anim Ecol 44:331–340
• 5. Benilov MS (2008) Bifurcations of current transfer through a collisional sheath with ionization and selforganization of glow cathodes. Phys Rev E 77:036408
• 6.Berryman A (2002) Population cycles: the case for trophic interactions. Oxford University Press, Oxford
• 7. Bödeker HU, Röttger MC, Liehr AW, Frank TD, Friedrich R, Purwins H-G (2003) Noise-covered drift bifurcation of dissipative solitons in a planar gas-discharge system. Phys Rev E 67:056220
• 8. Ciuchi S, de Pasquale F, Spagnolo B (1996) Self-regulation mechanism of an ecosystem in a non-Gaussian fluctuation regime. Phys Rev E 54:706–716
• 9. Gammaitoni L, Hänggi P, Jung P, Marchesoni F (1998) Stochastic resonance. Rev Mod Phys 70:223–287
• 10.García-Ojalvo J, Sancho JM (1999) Noise in spatially extended systems. Springer-Verlag, New York
• 11.Horsthemke W, Lefever R (1984) Noise-induced transitions. Springer-Verlag, New York
• 12. Laas T, Sauga A, Mankin R, Ainsaar A, Ugaste Ü, Rekker A (2006) Colored-noise-induced anomalous transport in periodic structures. Nukleonika 51;1:63–69
• 13. Linke H (ed) (2002) Special issue on “Ratchets and Brownian motors: basics, experiments and applications”.Appl Phys A 75:167–352
• 14. Mankin R, Ainsaar A, Haljas A, Reiter E (2002) Trichotomous-noise-induced catastrophic shifts in symbiotic ecosystems. Phys Rev E 65:051108
• 15. Mankin R, Ainsaar A, Reiter E (1999) Trichotomous noise-induced transitions. Phys Rev E 60:1374–1380
• 16. Mankin R, Haljas A, Tammelo R, Martila D (2003) Mechanism of hypersensitive transport in tilted sharp ratchets. Phys Rev E 68:011105
• 17. Mankin R, Laas T, Sauga A, Ainsaar A, Reiter E (2006) Colored-noise-induced Hopf bifurcations in predatorprey communities. Phys Rev E 74:021101
• 18. Mankin R, Laas T, Soika E, Ainsaar A (2007) Noisecontrolled slow-fast oscillations in predator-prey models with the Beddington functional response. Eur Phys J B 59:259–269
• 19. Mankin R, Sauga A, Ainsaar A, Haljas A, Paunel K (2004) Colored-noise-induced discontinuous transitions in symbiotic ecosystems. Phys Rev E 69:061106
• 20. Mankin R, Sauga A, Laas T, Soika E (2007) Environmental-fluctuations-induced slow-fast cycles in ratiodependent predator-prey systems. WSEAS Transactions on Systems 6:934–941
• 21. Mankin R, Sauga A, Laas T, Soika E (2007) Noisecontrolled relaxation oscillations in ratio-dependent predator-prey models. In: Proc of the 3rd WSEAS Int Conf on Mathematical Biology and Ecology, 17–19 January 2007, Gold Coast, Australia, 1:12–20
• 22. Martila D, Mankin R, Tammelo R, Sauga A, Reiter E (2006) Constructive influence of noise-flatness in correlation ratchets. Eur Phys J B 54:375–383
• 23. Pimenov VN, Gribkov VA, Dubrovsky AV et al. (2002) Influence of powerful pulses of hydrogen plasma upon materials in PF-1000 device. Nukleonika 47;4:155–162
• 24. Reimann P (2002) Brownian motors: noisy transport far from equilibrium. Phys Rep 361:57–265
• 25. Sauga A, Mankin R (2005) Addendum to colored-noiseinduced discontinuous transitions in symbiotic ecosystems.Phys Rev E 71:062103
• 26. Scheffer M, Carpenter S, Foley JA, Folke C, Walker B (2001) Catastrophic shifts in ecosystems. Nature 413:591–596
• 27.Spagnolo B, Valenti D, Fiasconaro A (2004) Noise in ecosystems: a short review. Math Biosci Eng 1:185–211