Predator-prey oscillations, synchronization and pattern formation in ecological systems

Analysis And Control Of Complex Nonlinear Processes In Physics, Chemistry And Biology

Volumn , Issue , 2007, Pages 397-427

  Blasius, Bernd ^a   Tönjes, Ralf ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85115731926     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812706911_0015     Document Type: Chapter

References (51)

1. R. May, Stability and Complexity in Model Ecosystems (Princeton University Press, 1973).
2. C. Elton & M. Nicholson. The ten-year cycle in numbers of the lynx in Canada. J. Anim. Ecol. 11, 215-244 (1942)
3. Keith, L. B. Wildlife’s ten year cycle. (University of Wisconsin Press, Madison, 1963).
4. Royama, T. Analytical Population Dynamics. (Chapman & Hall, London, 1992).
5. Moran, P. A. P. The statistical analysis of the Canadian lynx cycle. Aust. J. Ecol. 1, 291-298 (1953)
6. E. Ranta, and V. Kaitala, Travelling waves in vole population dynamics. Nature 390, 456 (1997).
7. Johnson, D. M., Bjrnstad, O. N. & Liebhold, A. M. Landscape geometry and traveling waves in the larch budmoth. Ecology Letters 7 967-974 (2004).
8. O. N. Bjørnstad, R. A. Ims, and X. Lambin. Spatial population dynamics: analyzing patterns and processes of population synchrony. Trends in Ecology and Evolution 14 427-432 (1999).
9. Liebhold, A., Walter, D. K. & Bjørnstad, O. N. Spatial synchrony in population dynamics. Annual Review of Ecology and Systematics. 35 467-490 (2004).
10. Blasius, B., & Stone, L., Nonlinearity and the Moran effect. Nature, 406, 846-847 (2000)
11. Volterra V. Fluctuations in abundance of a species considered mathematically. Nature 118 558-560 (1926).
12. Lotka A. J. Undamped oscillations derived from the law of mass action. J. Amer. Chem. Soc. 42 1595-1598 (1920).
13. Armstrong, R.A. The effects of predator functional response and prey productivity on predator-prey stability: A graphical approach. Ecology 57, 609-612 (1976)
14. Rosenzweig, M.L. & R.H. MacArthur. Graphical Representation and Stability Conditions of Predator-prey interactions. Am. Nat. 97, 209 (1963).
15. Rosenzweig, M.L. Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171, 385-387 (1971)
16. Gilpin, M.E. Enriched predator-prey systems: Theoretical stability. Science 177, 902-904 (1972)
17. May, R.M. (1972). Limit cycles in predator-prey communities. Science 177, 900-902.
18. Persson, A., Hansson, L.A., Brönmark, C, Lundberg, P., Pettersson, L.B., Greenberg, L., Nilsson, P.A., Nyström, P., Romare, P., & Tranvik, L. Effects of enrichment on simple aquatic food webs. Am. Nat. 157 654-669 (2001).
19. Fußmann G.F. & Blasius B. Community response to enrichment is highly sensitive to model structure. Biol. Lett. 1 9-12 (2005).
20. Holling, CS. The components of predation as revealed by a study of small-mammal predation of the European Pine Sawfly. The Canadian Entomologist 91, 293-320 (1959)
21. Ivlev, V.S. Experimental Ecology of the Feeding of Fishes. Yale University Press, New Haven (1961).
22. Myerscough, M.R., Darwen, M.J. & Hogarth, W.L. 1996 Stability, persistence and structural stability in a classical predator-prey model. Ecol. Model. 89, 31-42.
23. Wood, S.N. & Thomas, M.B. 1999 Super-sensitivity to structure in biological models. Proc. R. Soc. Lond. B. 266, 565-570.
24. Gross, T., Ebenhöh, W. & Feudel, U. Enrichment and foodchain stability: the impact of different forms of predator-prey interaction. J. Theor. Biol. 227 349-358 (2004).
25. Ludwig, D., D.D. Jones & CS. Holling Qualitative analysis of insect, outbreak systems: the spruce budworm and forest. J. Anim. Ecol. 47 315-332 (1978).
26. Lindner, B., Garcia-Ojalvo, J., Neiman, A. & Schimansky-Geier, L. Effects of noise in excitable systems. Phys. Rep. 392 321-424 (2004).
27. A.S. Pikovsky & J. Kurths. Coherence Resonance in a Noise-Driven Excitable System. Phys. Rev. Lett. 78 775-778 (1997).
28. B. Blasius, A. Huppert & L. Stone. Complex dynamics and phase synchronization in spatially extended ecological systems. Nature 399, 354-359 (1999)
29. B. Blasius & L. Stone. Chaos and phase synchronization in ecological sys- terns. Int. J. Bif. and Chaos 10, 2361-2380 (2000)
30. O.E. Rössler, Phys. Lett. A 57, 97 (1976).
31. M.G. Rosenblum, A.S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).
32. A. S. Pikovsky, M.G. Rosenblum, and J. Kurths, Synchronization, a Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001).
33. B. Blasius, E. Montbrio, & J. Kurths. Anomalous phase synchronization in populations of nonidentical oscillators. Phys. Rev. E 67, 035204 (2003).
34. E. Montbrio & B. Blasius. Using nonisochronicity to control synchronization in ensembles of non-identical oscillators. Chaos 13, 291-308 (2003)
35. B. Blasius. Anomalous phase synchronization in two asymmetrically coupled oscillators in the presence of noise. Phys. Rev. E 72 066216 (2005).
36. A. N. Zaikin and A. M. Zhabotinsky, Nature 255, 535 (1970);
37. P. S. Hagan, Adv. Appl. Math. 2, 400 (1981).
38. Y. Kuramoto Chemical oscillations, waves and turbulence (Springer, Berlin, 1985).
39. A. S. Mikhailov, Foundations of Synergetics I (Springer, Berlin, 1994).
40. A. S. Mikhailov and A. Engel, Physics Letters A 117, 257 (1986).
41. H. Sakaguchi, S. Shinomoto and Y. Kuramoto, Prog, of Theor. Phys. 79, 1069 (1988).
42. B. Blasius & R. Tönjes. Quasiregular concentric waves in heterogeneous lattices of coupled oscillators. Phys. Rev. Lett. 95 084101 (2005).
43. K. Koppel and G.B. Ermentrout, Comm. Pure and Appl. Math. 39, 623 (1986);
44. SIAM J. Appl. Math. 50, 1014 (1990).
45. S.C. Manrubia, A.S. Mikhailov, and D.H. Zanette, Emergence of Dynamical Order: Synchronization Phenomena in Complex Systems (World Scientific, Singapore, 2004).
46. A. H. Cohen, P. J. Holmes and R. H. Rand, J. Math. Biology 13, 345 (1982).
47. P.W. Anderson, Phys. Rev. 109, 1492 (1958)
48. M. Janssen, Phys. Rep. 295, 1 (1998).
49. R. Kapral and K. Showalter (eds.) Chemical Waves and Patterns (Kluwer Academic Publishers, Dordrecht, 1995).
50. T. Shinbrot and F. J. Muzzio, Nature 410, 251 (2001).
51. S. Kadar, J. Wang and K. Showalter, Nature 391, 770 (1998).