Stochastic sensitivity analysis of noise-induced excitement in a prey–predator plankton system

References

• Allen , LJ S . 2003 . “ An introduction to the stochastic process with applications to biology ” . Upper Saddle River (NJ) : Pearson .
   Google Scholar
• Anishchenko , V S , Astakhov , V V , Neiman , A B , Vadivasova , T E and Schimansky-Geier , L . 2007 . Nonlinear dynamics of chaotic and stochastic systems. Tutorial and modern development , Berlin (Germany) : Springer-Verlag .
   Google Scholar
• Baltanas , J P , Zaikin , A , Feudel , F , Kurths , J and Sanjuan , MA F . 2002 . Noise-induced effects in tracer dynamics . Phys Lett A. , 297 : 396 – 401 .
   Web of Science ®Google Scholar
• Bashkirtseva , I A and Ryashko , L B . 2000 . Sensitivity analysis of the stochastically and periodically forced Brusselator . Physica A. , 278 : 126 – 139 .
   Web of Science ®Google Scholar
• Bashkirtseva , I and Ryashko , L . 2004 . Stochastic sensitivity of 3D-cycles . Math Comput Simul. , 66 : 55 – 67 .
   Web of Science ®Google Scholar
• Bashkirtseva , I and Ryashko , L . 2009 . Constructive analysis of noise-induced transitions for coexisting periodic attractors of Lorenz model . Phys Rev E. , 79 : 041106 – 041114 .
   Web of Science ®Google Scholar
• Bashkirtseva , I and Ryashko , L . 2011 . Sensitivity analysis of stochastic attractors and noise-induced transitions for population model with Allee effect . Chaos. , 21 : 047514-8
   Web of Science ®Google Scholar
• Bashkirtseva , I , Ryashko , L and Stikhin , P . 2010 . Noice-induced backward bifurcations of stochastic 3D-cycles . Fluct Noise Lett. , 9 : 89 – 106 .
   Web of Science ®Google Scholar
• Bazykin , A D . 1998 . “ Nonlinear dynamics of interacting populations ” . Singapore : World Scientific .
   Google Scholar
• Berglund , N , Gentz , B and Kuehn , C . 2012 . Hunting french ducks in a noisy environment . J Differ Equ. , 252 : 4786 – 4841 .
   Web of Science ®Google Scholar
• Berglund N, Landon D. 2011. Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model. e-print arXiiv: 1105.1278v3.
   Google Scholar
• Biktashev , V Z , Brindley , J and Horwood , J W . 2003 . Phytoplankton blooms and fish recruitment rate . J Plankton Res. , 25 : 21 – 33 .
   Web of Science ®Google Scholar
• Clother , R and Brindley , J . 1999 . Excitability of an age-structured population . J Math Biol. , 39 : 377 – 421 .
   PubMed Web of Science ®Google Scholar
• Dembo , M and Zeitouni , O . 1995 . “ Large deviations techniques and applications ” . Boston (MA) : Jones and Bartlett Publishers .
   Google Scholar
• Dennis , B . 2002 . Allee effects in stochastic populations . Oikos. , 96 : 389 – 401 .
   Web of Science ®Google Scholar
• Freidlin , M I and Wentzell , A D . 1984 . “ Random perturbations of dynamical systems ” . New York (NY : Springer .
   Google Scholar
• Freund , J A , Mieruch , S , Scholze , B , Wiltshire , K and Feudel , U . 2006 . Bloom dynamics in a seasonally forced phytoplankton-zooplankton model: Trigger mechanisms and timing effects . Ecol Compl. , 3 : 129 – 139 .
   Google Scholar
• Holling , C S . 1959 . The components of predation as revealed by a study of small mammal predation of the European Pine Sawfly . Can Entomol. , 91 : 293 – 320 .
   Google Scholar
• Horsthemke , W and Lefever , R . 1984 . “ Noise-induced transitions ” . Berlin (Germany) : Springer .
   Google Scholar
• Huppert , A , Olinky , R and Stone , L . 2004 . Bottom-up excitable models of phytoplankton blooms . Bull Math Biol. , 66 : 865 – 878 .
   Web of Science ®Google Scholar
• Kraut , S , Feudel , U and Grebogi , C . 1999 . Preference of attractors in noisy multistable systems . Phys Rev E. , 59 : 5253 – 5260 .
   Web of Science ®Google Scholar
• Li , D. , Xu , W. , Guo , Y. and Xu , Y. 2011 . Fluctuations induced extinction and stochastic resonance effect in a model of tumor growth with periodic treatment . Phys Lett A. , 375 : 886 – 890 .
   Web of Science ®Google Scholar
• Lindner , B , Garcia-Ojalvo , J , Neiman , A and Schimansky-Geier , L . 2004 . Effects of noise in excitable systems . Phys Rep. , 392 : 321 – 424 .
   Web of Science ®Google Scholar
• Lindner , B and Schimansky-Geier , L . 1999 . Analytical approach to the stochastic FitzHugh-Nagumo system and coherence resonance . Phys Rev E. , 60 : 7270 – 7276 .
   Web of Science ®Google Scholar
• May , R M . 2001 . Stability and complexity in model ecosystems , Princeton (NJ) : Princeton University Press .
   Google Scholar
• Mil'shtein , G N and Ryashko , L B . 1995 . A first approximation of the quasipotential in problems of the stability of systems with random non-degenerate perturbations . J Appl Math Mechs. , 59 : 47 – 56 .
   Web of Science ®Google Scholar
• Morozov , A and Petrovskii , S . 2009 . Excitable population dynamics, biological control failure, and spatiotemporal pattern formation in a model ecosystem . Bull Math Biol. , 71 : 863 – 887 .
   PubMed Web of Science ®Google Scholar
• Muratov , C B and Vanden-Eijnden , E . 2008 . Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle . Chaos. , 18 : 015111
   Web of Science ®Google Scholar
• Murray , J D . 1989 . Mathematical biology , Heidelberg (Germany) : Springer .
   Google Scholar
• Pikovsky , A S and Kurths , J . 1997 . Coherence resonance in a noise-driven excitable system . Phys Rev Lett. , 78 : 775 – 778 .
   Web of Science ®Google Scholar
• Ridolfi , L , D'Odorico , P and Laio , F . 2011 . “ Noise-induced phenomena in the environmental sciences ” . Cambridge (UK) : Cambridge University Press .
   Google Scholar
• Rietkerk , M , Dekker , S C , de Ruiter , P C and van de Koppel , J . 2004 . Self-organized patchiness and catastrophic shifts in ecosystems . Science. , 305 : 1926 – 1929 .
   PubMed Web of Science ®Google Scholar
• Ryashko , L , Bashkirtseva , I , Gubkin , A and Stikhin , P . 2009 . Confidence tori in the analysis of stochastic 3D-cycles . Math Comput Simul. , 80 : 256 – 269 .
   Web of Science ®Google Scholar
• Scheffer , M , Carpenter , S , Foley , J A , Folke , C and Walker , B . 2001 . Catastrophic shifts in ecosystems . Nature. , 413 : 591 – 596 .
   PubMed Web of Science ®Google Scholar
• Sieber , M , Malchow , H and Schimansky-Geier , L . 2007 . Constructive effects of environmental noise in an excitable prey-predator plankton system with infected prey . Ecological Complexity. , 4 : 223 – 233 .
   Web of Science ®Google Scholar
• Spagnolo , B , Valenti , D and Fiasconaro , A . 2004 . Noise in ecosystems: a short review . Math. Biosci Eng. , 1 : 185 – 211 .
   PubMed Web of Science ®Google Scholar
• Sun , G Q , Jin , Z , Li , L and Liu , Q X . 2009 . The role of noise in a predator-prey model with Allee effect . J Biol Phys. , 35 : 185 – 196 .
   Web of Science ®Google Scholar
• Truscott , J E and Brindley , J . 1994 . Ocean plankton populations as excitable media . Bull Math Biol. , 56 : 981 – 998 .
   Web of Science ®Google Scholar
• Volkov , E I , Ullner , E , Zaikin , A A and Kurths , J . 2003 . Frequency-dependent stochastic resonance in inhibitory coupled excitable systems . Phys Rev E. , 68 : 026214 – 026220 .
   Web of Science ®Google Scholar