Synchrony & chaos in patchy ecosystems

Bulletin of Mathematical Biology

Volumn 66, Issue 6, 2004, Pages 1909-1931

  Hillary, R M ^a   Bees, M A ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; CELL DIVISION; CYTOLOGY; ECOSYSTEM; KINETICS; MATHEMATICAL COMPUTING; NONLINEAR SYSTEM; PHYSIOLOGY; PHYTOPLANKTON; ZOOPLANKTON;

ANIMALS; CELL DIVISION; ECOSYSTEM; KINETICS; MATHEMATICAL COMPUTING; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; PHYTOPLANKTON; ZOOPLANKTON;

EID: 7444253963     PISSN: 00928240     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.bulm.2004.05.006     Document Type: Article

References (31)

1. Abarbanel H.D.I., Rulkov N.F., Sushchik M.M. Generalized synchronization of chaos: the auxiliary systems approach. Phys. Rev. E. 53:1996;4258-4535
2. Alexander J.C., Yorke J.A., You Z., Kan I. Riddled basins. Int. J. Bifurcation Chaos. 2:1992;795-813
3. Allen J., Schaffer W., Rosko D. Chaos reduces species extinction by amplifying local population noise. Nature. 364:1993;229-234
4. Ashwin P., Buescu J., Stewart I. Bubbling of attractors and synchronisation of chaotic oscillators. Phys. Lett. A. 193:1994;126-139
5. Belykh B., Belykh I.V., Mosekilde E. Cluster synchronization modes in an ensemble of coupled chaotic oscillators. Phys. Rev. E. 63:2001;036216
6. Blasius B., Stone L. Chaos and phase synchronization in ecological systems. Int. J. Bifurcation Chaos. 10:2000;2361-2380
7. Blasius B., Stone L. Nonlinearity and the Moran effect. Nature. 406:2000;846-847
8. Dunn M.R., Pawson M.G. The stock structure and migrations of plaice populations on the west coast of England and Wales. J. Fish Biol. 61:2002;360-393
9. Eckmann J.-P., Ruelle D. Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57:1985;617-656
10. Edwards A.M., Bees M.A. Generic dynamics of a simple plankton population model with a non-integer exponent of closure. Chaos Solitons Fractals. 12:2001;289-300
11. Edwards A.M., Brindley J. Oscillatory behaviour in a three component plankton population model. Dyn. Stab. Syst. 11:1996;347-370
12. Fox C.J., Planque B.P., Darby C.P. Synchrony in the recruitment time-series of plaice (Pleuronectes platessa L) around the United Kingdom and the influence of sea temperature. J. Sea. Res. 44:2002;159-168
13. Fujisaka H., Yamada T. Stability theory of synchronized motion in coupled-oscillator systems. Prog. Theor. Phys. 69:1983;32-48
14. Grenfell B.T., Wilson K., Finkelstädt B.F., Coulson T.N., Murray S., Albon S.D., Pemberton J.M., Clutton-Brock T.H., Crawley M.J. Noise and determinism in synchronized sheep dynamics. Nature. 394:1998;674-677
15. Hastings A., Powell T. Chaos in a three species food chain. Ecology. 72:1991;896-903
16. Hillary, R.M. (2003). Effects of turbulence and a patchy environment on the dynamics of plankton populations, PhD thesis, University of Surrey
17. Hillary R.M., Bees M.A. Plankton lattices and the role of chaos in plankton patchiness. Phys. Rev. E. 69:2004;031913
18. Hudson P.J., Cattadori I.M. The Moran effect: a cause of population synchrony. TREE. 14:1999;1-2
19. Josic K. Invariant manifolds and synchronization of coupled dynamical systems. Phys. Rev. Lett. 80:1998;3053-3056
20. Keith L.B. Wildlife's Ten Year Cycle. 1963;Cambridge University Press, Cambridge
21. Moran P.A.P. The statistical analysis of the Canadian lynx cycle. Aust. J. Zool. 1:1953;291-298
22. Ott E., Sommerer J.C. Blowout bifurcations: the occurrence of riddled basins and on-off intermittency. Phys. Lett. A. 188:1994;39-47
23. Pecora L.M. Synchronization conditions and desynchronizing patterns in coupled limit-cycle and chaotic systems. Phys. Rev. E. 58:1998;347-360
24. Pecora L.M., Carroll T.L. Synchronization in chaotic systems. Phys. Rev. Lett. 64:1990;821-825
25. Pecora L.M., Carroll T.L., Heagy J.F. Statistics for mathematical properties of maps between time series embeddings. Phys. Rev. E. 52:1995;3420-3439
26. Pikovsky A.S. On the interaction of strange attractors. Z. Phys. B. 55:1984;149-154
27. Pikovsky A.S., Rosenblum M.G., Osipov J.V., Kurths J. Phase synchronization of chaotic oscillators by external driving. Physica D. 104:1997;219-238
28. Rössler O.E. An equation for continuous chaos. Phys. Lett. A. 57:1976;397-398
29. Steele J.H., Henderson E.W. A simple plankton model. Am. Naturalist. 14:1981;157-183
30. Sughihara G., May R.M. Non-linear forecasting as a way of distinguishing chaos from measurement error. Nature. 344:1990;734-741
31. Wiggins S. Normally Hyperbolic Invariant Manifolds in Dynamical Systems. 1994;New York, Springer