Controlling chaos in ecology: From deterministic to individual-based models

Bulletin of Mathematical Biology

Volumn 61, Issue 6, 1999, Pages 1187-1207

  Solé, Ricard V ^a   Gamarra, Javier G P ^a,b   Ginovart, Marta ^a   López, Daniel ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b Forest Technology Center of Catalonia   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CHAOTIC DYNAMICS; CONTROL SYSTEM; ECOLOGY; ECOSYSTEM; MATHEMATICAL MODEL; MODEL; NOISE; POPULATION DYNAMICS; SIMULATION;

EID: 0032701815     PISSN: 00928240     EISSN: None     Source Type: Journal    
DOI: 10.1006/bulm.1999.0141     Document Type: Article

References (46)

1. Allen J. C., Schaffer W. M., Rosko D. Chaos reduces species extinction by amplifying local population noise. Nature. 364:1993;229-232.
2. Astakhov V. V., Ansihehenko V. S., Shabunin A. V. Controlling spatiotemporal chaos in a chain of coupled logistic maps. IEEE Trans. Circuits Syst. 1. 42:1995;352-357.
3. Bascompte J., Solé R. V. Rethinking complexity: modelling spatiotemporal dynamics in ecology. Trends Ecol. Evol. 10:1995;361-366.
4. Berryman A. A., Millstein J. A. Are ecological systems chaotic - and if not, why not? Trends Ecol. Evol. 4:1989;26-28.
5. Constantino R. F., Cushing J. M., Dennis B., Desharnais R. A. Experimentally induced transitions in the dynamic behaviour of insect populations. Nature. 375:1995;227-230.
6. Constantino R. F., Desharnais R. A., Cushing J. M., Dennis B. Chaotic dynamics in an insect populations. Science. 275:1997;389-391.
7. Dennis B., Desharnais R. A., Cushing J. M., Constantino R. F. Transitions in population dynamics: equilibria to periodic cycles to aperiodic cycles. J. Anim. Ecol. 66:1997;704-729.
8. Ditto W. L., Rauseo S. N., Spano M. L. Experimental control of chaos. Phys. Rev. Lett. 65:1990;3211-3214.
9. Ditto W. L., Spano M. L., Lindner J. F. Techniques for the control of chaos. Physica D. 86:1995;198-211.
10. Doebeli M. The evolutionary advantage of controlled chaos. Proc. R. Soc. Lond. B. 254:1993;281-285.
11. Doebeli M., Ruxton G. D. Controlling spatiotemporal chaos in metapopulations with long-range dispersal. Bull. Math. Biol. 59:1997;497-515.
12. Fox R. F., Keitzer J. E. Effect of molecular fluctuations on the description of chaos by microvariable equations. Phys. Rev. Lett. 64:1990;249-251.
13. Garfinkel A., Spano M. L., Ditto W. L., Weiss J. N. Controlling cardiac chaos. Science. 257:1992;1230-1235.
14. Godfray H. C. J., Blythe S. P. Complex dynamics in multispecies communities. Phil. Trans. R. Soc. Lond. B. 330:1990;221-233.
15. Güemez J., Matías M. A. Control of chaos in uni-dimensional maps. Phys. Lett. A. 181:1993;29-32.
16. Hassell M. P., Lawton J. H., May R. M. Patterns of dynamical behavior in single-species populations. J. Anim. Ecol. 45:1976;471-486.
17. Hastings A. Complex interactions between dispersal and dynamics, lessons from coupled logistic equations. Ecology. 74:1993;1362-1372.
18. Hastings A., Powell T. Chaos in a three-species food chain. Ecology. 72:1991;896-903.
19. Judson O. P. The rise of the individual-based model in ecology. Trends Ecol. Evol. 9:1994;9-14.
20. Kot M., Sayler G. S., Schultz T. W. Complex dynamics in a model microbial system. Bull. Math. Biol. 54:1992;619-648.
21. Lomnicki A. Avoiding chaos. Trends Ecol. Evol. 4:1989;239.
22. May R. M. Biological populations with nonoverlapping generations: stable points, stable cycles and chaos. Science. 186:1974;645-647.
23. May R. M. Simple mathematical models with very complicated dynamics. Nature. 261:1976;459-467.
24. May R. M., Oster G. F. Bifurcations and dynamic complexity in simple ecological models. Am. Nat. 110:1976;573-599.
25. McCallum H. I. Effects of inmigration on chaotic population dynamics. J. Theor. Biol. 154:1992;277-284.
26. McCann K., Hastings A., Huxel G. R. Weak trophic interactions and the balance of nature. Nature. 395:1998;794-798.
27. Nisbet R., Blythe S., Gurney B., Metz H., Stokes K. Avoiding chaos. Trends Ecol. Evol. 4:1989;238-239.
28. Ott E., Grebogi C., Yorke J. A. Controlling chaos. Phys. Rev. Lett. 64:1990;1196-1199.
29. Parthasarathy S., Sinha S. Controlling chaos in unidimensional maps using constant feedback. Phys. Rev. E. 51:1995;6239-6242.
30. Peeters P., Nicolis G. Intrinsic fluctuations in chaotic dynamics. Physica A. 188:1992;426-435.
31. Petrov V., Gáspár V., Masere J., Showalter K. Controlling chaos in the Belousov-Zhabotinsky reaction. Nature. 361:1993;240-243.
32. Pimm S. L. The Balance of Nature?: Ecological Issues in the Conservation of Species and Communities. 1991;University of Chicago Press, Chicago.
33. Ricker W. E. Stock and recruitment. Fish. Res. Board. Canada. 11:1954;559-623.
34. Rinaldi S., Muratori S., Kuznetsov Y. Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities. Bull. Math. Biol. 55:1993;15-35.
35. Ringelberg J. Properties of an aquatic microecosystem. II. Steady-state phenomena in the autotrophic subsystem. Helgoländer Meeresunters. 30:1977;134-143.
36. Rohani P., Earn D. J. D. Chaos in a cup of flour. Trends Ecol. Evol. 12:1997;171.
37. Schaffer W. M. Stretching and folding in lynx for returns: evidence for a strange attractor in nature? Am. Nat. 124:1984;798-820.
38. Schaffer W. M., Kot M. Chaos in ecological systems: the coals that Newcastle forgot. Trends Ecol. Evol. 1:1986;58-63.
39. Scheffer M. Should we expect strange attractors behind plankton dynamics-and if so, should we bother? J. Plankton. Res. 13:1991;1291-1305.
40. Schiff S. J., Jerger K., Duong D. H., Chang T., Spano M. L., Ditto W. L. Controlling chaos in the brain. Nature. 370:1994;615.
41. Solé R. V., Gamarra J. G. P. Chaos, dispersal and extinction in coupled ecosystems. J. Theor. Biol. 193:1998;539-541.
42. Solé R. V., Menéndez de la Prida L. Controlling chaos in discrete neural networks. Phys. Lett. A. 199:1995;65-69.
43. Solé R. V., Valls J. Nonlinear phenomena and chaos in a Monte Carlo simulated microbial ecosystem. Bull. Math. Biol. 54:1992;939-955.
44. Stone L. Period-doubling reversals and chaos in simple ecological models. Nature. 365:1993;617-620.
45. Tilman D., Wedin D. Oscillations and chaos in the dynamics of a perennial grass. Nature. 353:1991;653-655.
46. Wilson W. G. Resolving discrepancies between deterministic population models and individual-based simulations. Am. Nat. 151:1998;116-134.