Dynamical complexity of a spatial predator-prey model with migration

Ecological Modelling

Volumn 219, Issue 1-2, 2008, Pages 248-255

  Sun, Gui Quan ^a   Jin, Zhen ^a   Liu, Quan Xing ^a   Li, Li ^a  

^a NORTH UNIVERSITY OF CHINA   (China)

Author keywords

Migration; Predator Prey; Synchrony; Travelling pattern

Indexed keywords

COMPUTER SIMULATION; DIFFUSION; ECOLOGY; ELECTRIC NETWORK ANALYSIS; SEMICONDUCTOR DOPING;

DIFFUSION COEFFICIENTS; DYNAMIC COMPLEXITIES; DYNAMICAL COMPLEXITIES; ECOLOGICAL INTERACTIONS; FIELD OBSERVED; MIGRATION; MODELING; NUMERICAL SIMULATIONS; PATTERN FORMATIONS; PREDATOR-PREY; SPATIAL PATTERNS; SYNCHRONY; THEORETICAL ANALYSES; TRAVELLING PATTERN; TRAVELLING PATTERNS;

ECOSYSTEMS;

COMPLEXITY; ECOLOGICAL MODELING; MIGRATION; NUMERICAL MODEL; PREDATOR-PREY INTERACTION; SYNCHRONY; TRAVEL BEHAVIOR;

EID: 54049134367     PISSN: 03043800     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ecolmodel.2008.08.009     Document Type: Article

References (43)

1. Abrams P.A., and Ginzburg L.R. The nature of predation: prey dependent, ratio dependent or neither?. Trends Ecol. Evol. 15 (2000) 337-341
2. Alonso D., Bartumeus F., and Catalan J. Mutual interference between predators can give rise to Turing spatial patterns. Ecology 83 1 (2002) 28-34
3. Andresen P., Bache M., Mosekilde E., Dewel G., and Borckmanns P. Stationary space-periodic structures with equal diffusion coefficients. Phys. Rev. E 60 (1999) 297-301
4. Arditi R., and Ginzburg L.R. Coupling in predator-prey dynamics: ratio dependence. J. Theor. Biol. 139 (1989) 311-326
5. Baurmann M., Gross T., and Feudel U. Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations. J. Theor. Biol. 245 (2007) 220-229
6. Blasius B., and To{combining double acute accent}njes R. Analysis and Control of Complex Nonlinear Processes in Physics (2007), World Scientific, Singapoore
7. Comins H.N., Hassell M.P., and May R.M. The spatial dynamics of host-parasitoid systems. J. Anim. Ecol. 61 (1992) 735-748
8. Cushing J.M., Costantino R.F., Dennis B., Desharnais R.A., and Henson S.M. Chaos in Ecology: Experimental Nonlinear Dynamics (2003), Academic, San Diego
9. Fraser D.F., and Gilliam J.F. Nonlethal impacts of predator invasion-facultative suppression of growth and reproduction. Ecology 73 (1992) 959-970
10. Garvie M.R. Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in matlab. Bull. Math. Biol. 69 (2007) 931-956
11. Ginzburg L.R. Assuming reproduction to be a function of consumption raises doubts about some popular predator-prey models. J. Anim. Ecol. 67 (1998) 325-327
12. Gurney W.S.C., Veitch A.R., Cruickshank I., and Mcgeachin G. Circles and spirals: population persistence in a spatially explicit predator-prey model. Ecology 79 7 (1998) 2516-2530
13. Hengeveld R. Dynamics of Biological Invasions (1989), Chapman and Hall, London
14. Hui C., Li Z., and xia Yue D. Metapopulation dynamics and distribution, and environmental heterogeneity induced by niche construction. Ecol. Model. 177 (2004) 107-118
15. Huu T.N., Lett C., Poggiale J., and Auger P. Effect of movement frequency on global host-parasitoid spatial dynamics with unstable local dynamics. Ecol. Model. 197 (2006) 290-295
16. Huygens C.H. Horoloqium Oscilatorium (1673), Parisiis, France
17. Kuang Y., and Beretta E. Global qualitative analysis of a ratio-dependent predator-prey system. J. Math. Biol. 36 4 (1998) 389-406
18. Kuznetsov S.P., Mosekilde E., Dewel G., and Borckmans P. Absolute and convective instabilities in a one-dimensional brusselator flow model. J. Chem. Phys. 106 18 (1997) 7609-7616
19. Li Z.-Z., Gao M., Hui C., Zhuo Han X., and Shi H. Impact of predator pursuit and prey evasion on synchrony and spatial patterns in metapopulation. Ecol. Model. 185 (2005) 245-254
20. MacArthur R. Population ecology of some warblers of northeastern coniferous forests. Ecology 39 (1958) 599-619
21. Malchow H. Motional instabilities in predator-prey systems. Ecology 204 4 (2000) 639-647
22. Medvinsky A.B., Petrovskii S.V., Tikhonova I.A., Malchow H., and Li B.-L. Spatio-temporal complexity of plankton and fish dynamics in simple model ecosystems. SIAM Rev. 44 3 (2002) 311-370
23. Morozov A., Petrovskii S., and Li B.-L. Bifurcations and chaos in a predator-prey system with the allee effect. Proc. R. Soc. Lond. B 271 (2004) 1407-1414
24. Morozov A., Petrovskii S., and Li B.-L. Spatiotemporal complexity of patchy invasion in a predator-prey system with the allee effect. J. Theor. Biol. 238 (2006) 18-35
25. Murray J.D. Mathematical Biology II: Spatial Models and Biomedical Applications (2003), Springer, New York
26. Neubert M., Caswell H., and Murray J. Transient dynamics and pattern formation: reactivity is necessary for Turing instabilities. J. Theor. Biol. 175 (2002) 1-11
27. Nilssen K.T., Grotnes P.E., and Haug T. The effect of invading harp seals (phoca-groenlandica) on local coastal fish stocks of North Norway. Fisheries Res. 13 (1992) 25-37
28. Nowak M.A., and May R.M. Evolutionary games and spatial chaos. J. Anim. Ecol. 359 (1992) 826-829
29. Petrovskii S., and Li B.-L. An exactly solvable model of population dynamics with density-dependent migrations and the allee effect. Math. Biosci. 186 (2003) 79-91
30. Petrovskii S., Li B.-L., and Malchow H. Transition to chaos can resolve the paradox of enrichment. Ecol. Complex. 1 1 (2004) 37-47
31. Petrovskii S., Malchow H., and Li B.-L. An exact solution of a diffusive predator-prey system. Proc. R. Soc. A 461 (2005) 1029-1053
32. Petrovskii S., Morozov A., and Li B.-L. Regimes of biological invasion in a predator-prey system with the allee effect. Bull. Math. Biol. 67 (2005) 637-661
33. Petrovskii S.V., Morozov A.Y., and Venturino2 E. Allee effect makes possible patchy invasion in a predator-prey system. Ecol. Lett. 5 (2002) 345-352
34. Robinson J.V., and Wellborn G.A. Ecological resistance to the invasion of a freshwater clam, Corbiucula luminea: fish predation effects. Oecologia 77 (1988) 445-452
35. Segel L., and Jackson J. Dissipative structure: an explanation and an ecological example. J. Theor. Biol. 37 (1972) 545-559
36. Sherratt J.A. Periodic travelling waves in cyclic predator-prey systems. Ecol. Lett. 4 (1995) 30-37
37. Sherratt J.A., Eagan B.T., and Lewis M.A. Oscillations and chaos behind predator-prey invasion: mathematical artifact or ecological reality?. Philos. Trans. R. Soc. Lond. B 352 (1997) 21-38
38. Sherratt J.A., Lambin X., Thomas C.J., and Sherratt T.N. Generation of periodic waves by landscape features in cyclic predator-prey systems. Proc. R. Soc. Lond. B 269 (2002) 327-334
39. Turing A.M. The chemical basis of morphogenesis. Philos. Trans. R. Soc. Lond. B 237 (1952) 37-72
40. Wang W., Liu Q.X., and Jin Z. Spatiotemporal complexity of a ratio-dependent predator-prey system. Phys. Rev. E 75 (2007) 051913
41. Wilson W., and Abrams P. Coexistence of cycling and dispersing consumer species: Armstrong and Mcgehee in space. Am. Nat. 165 2 (2005) 193-205
42. Xiao D.M., and Jennings L.S. Bifurcations of a ratio-dependent predator-prey system with constant rate harvesting. SIAM J. Appl. Math. 65 3 (2005) 737-753
43. Zhang F., Li Z., and Hui C. Spatiotemporal dynamics and distribution patterns of cyclic competition in metapopulation. Ecol. Model. 193 (2006) 721-735