Free Access
Issue
Math. Model. Nat. Phenom.
Volume 10, Number 2, 2015
Ecology
Page(s) 130 - 140
DOI https://doi.org/10.1051/mmnp/201510209
Published online 02 April 2015
  1. L. J. S. Allen. An introduction to the stochastic process with applications to biology. Pearson, Upper Saddle River, NJ, 2003. [Google Scholar]
  2. I. Bashkirtseva, L. Ryashko. Stochastic sensitivity of 3D-cycles. Math. Comp. Sim., 66 (2004), 55–67. [Google Scholar]
  3. I. Bashkirtseva, G. Chen, L. Ryashko. Stabilizing stochastically-forced oscillation generators with hard excitement: a confidence-domain control approach. Eur. Phys. J. B, 86 (2013), 437. [CrossRef] [EDP Sciences] [Google Scholar]
  4. A. A. Berryman. Stabilization or regulation: what it all means!. Oecologia, 86 (1991), 140–143. [CrossRef] [PubMed] [Google Scholar]
  5. A. A. Berryman. Limiting factors and population regulation. Oikos, 105 (2004), 667–670. [CrossRef] [Google Scholar]
  6. A. J. Black, A. J. McKane. Stochastic formulation of ecological models and their applications. Trends in Ecology and Evolution, 27 (2012), 337–345. [CrossRef] [Google Scholar]
  7. R. P. Blackshaw, S. V. Petrovskii. Limitation and regulation of ecological populations: a meta-analysis of Tipula paludosa field data. Math. Model. Nat. Phenom., 2 (2007), 46–62. [CrossRef] [EDP Sciences] [Google Scholar]
  8. S. R. Carpenter, L. H. Gunderson. Coping with collapse: ecological and social dynamics in ecosystem management. BioScience, 51 (2001), 451. [CrossRef] [Google Scholar]
  9. O. Chichigina, D. Valenti, B. Spagnolo. A simple noise model with memory for biological systems. Fluctuation and Noise Letters, 5 (2) (2005), L243–L250. [Google Scholar]
  10. M. Dembo, O. Zeitouni. Large deviations techniques and applications. Jones and Bartlett Publishers, Boston, 1995. [Google Scholar]
  11. C. Folke, T. Hahn, P. Olsson, J. Norberg. Adaptive governance of social-ecological systems. Annual Review of Environment and Resources, 30 (2005), 441–473. [CrossRef] [Google Scholar]
  12. M. I. Freidlin, A. D. Wentzell. Random perturbations of dynamical systems. Springer, New York, 1984. [Google Scholar]
  13. E. González-Olivares, A. Rojas-Palma. Allee effect in Gause type predator-prey models: existence of multiple attractors, limit cycles and separatrix curves. A Brief Review. Math. Model. Nat. Phenom., 8 (2013), 143–164. [CrossRef] [EDP Sciences] [Google Scholar]
  14. C. S. Holling. The functional response of predator to prey density and its role in mimicry and population regulation. Mem. Entomol. Soc. Canada, 45 (1965), 1–60. [CrossRef] [Google Scholar]
  15. G. N. Mil’shtein, L. B. Ryashko. A first approximation of the quasipotential in problems of the stability of systems with random non-degenerate perturbations. J. Appl. Maths. Mechs. 59 (1995), 47–56. [Google Scholar]
  16. S. Petrovskii, A. Morozov, B. -L. Li. Regimes of biological invasion in a predator-prey system with the Allee effect. Bull. Math. Biol., 67 (2005), 637–661. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  17. L. Ridolfi, P. D’Odorico, F. Laio. Noise-induced phenomena in the environmental sciences. Cambridge University Press, Cambridge, 2011. [Google Scholar]
  18. M. Rietkerk, S. C. Dekker, P. C. de Ruiter, J. van de Koppel. Self-organized patchiness and catastrophic shifts in ecosystems. Science, 305 (2004), 1926–1929. [CrossRef] [PubMed] [Google Scholar]
  19. L. B. Ryashko, I. A. Bashkirtseva. On control of stochastic sensitivity. Automation and Remote Control, 69 (2008), 1171–1180. [CrossRef] [MathSciNet] [Google Scholar]
  20. L. Ryashko, I. Bashkirtseva. Stochastic sensitivity analysis of noise-induced excitement in a prey-predator plankton system. Frontiers in Life Science, 5 (2011) 141–148. [CrossRef] [Google Scholar]
  21. M. Scheffer, S. Carpenter, J. A. Foley, C. Folke, B. Walker. Catastrophic shifts in ecosystems. Nature, 413 (2001), 591–596. [CrossRef] [PubMed] [Google Scholar]
  22. B. Spagnolo, D. Valenti, A. Fiasconaro. Noise in ecosystems: a short review. Math. Biosci Eng. 1 (2004), 185–211. [Google Scholar]
  23. D. Valenti, L. Schimansky-Geier, X. Sailer, B. Spagnolo. Moment equations for a spatially extended system of two competitive species. Eur. Phys. J. B 50 (2006), 199–203. [CrossRef] [EDP Sciences] [Google Scholar]
  24. D. Valenti, G. Augello, B. Spagnolo. Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise. Eur. Phys. J. B, 65 (2008), 443–451. [CrossRef] [EDP Sciences] [Google Scholar]

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