Can noise induce chaos?

Oikos

Volumn 102, Issue 2, 2003, Pages 329-339

  Dennis, Brian ^a   Desharnais, Robert A ^b   Cushing, J M ^c   Henson, Shandelle M ^d   Costantino, R F ^c  

^a UNIVERSITY OF IDAHO   (United States)

^b CALIFORNIA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF ARIZONA   (United States)

^d ANDREWS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS; NOISE; POPULATION MODELING; STOCHASTICITY;

EID: 0042259193     PISSN: 00301299     EISSN: None     Source Type: Journal    
DOI: 10.1034/j.1600-0706.2003.12387.x     Document Type: Review

References (73)

1. Alligood, K. T., Sauer, T. D. and Yorke, J. A. 1997. Chaos: an introduction to dynamical systems. - Springer-Verlag.
2. Bailey, B. A., Ellner, S. and Nychka, D. W. 1997. Chaos with confidence: asymptotics and applications of local Lyapunov exponents. - In: Cutler, C. D. and Kaplan, D. T. (eds), Nonlinear dynamics and time series: building a bridge between the natural and statistical sciences. Fields Institute Communications. Vol. 110. Am. Math. Soc, pp. 115-133.
3. Bartlett, M. S. 1990. Chance or chaos? (with discussion). - J. R. Statist. Soc. A 52: 321-347.
4. Berliner, L. M. 1992. Statistics, probability, and chaos. - Statist. Sci. 7: 69-122.
5. Berryman, A. A. 1991. Chaos in ecology and resources management: what causes it and how to avoid it. - In: Logan, J. and Hain, F. P. (eds), Chaos and insect ecology. Virginia Experiment Station Information Series 91-3, Virginia Polytechnic Inst. and State Univ., pp. 23-38.
6. Berryman, A. A. and Millstein, J. A. 1989. Are ecological systems chaotic - and if not, why not. - Trends Ecol. Evol. 4: 26-28.
7. Costantino, R. F. and Desharnais, R. A. 1981. Gamma distributions of adult numbers for Tribolium populations in the regions of their steady states. - J. Anim. Ecol. 50: 667-681.
8. Costantino, R. F., Cushing, J. M., Dennis, B. and Desharnais, R. A. 1995. Experimentally induced transitions in the dynamic behavior of insect populations. - Nature 375: 227-230.
9. Costantino, R. F., Desharnais, R. A., Cushing, J.M. and Dennis, B. 1997. Chaotic dynamics in an insect population. - Science 275: 389-391.
10. Costantino, R. F., Cushing, J. M., Dennis, B. et al. 1998. Resonant population cycles in temporally fluctuating habitats. - Bull. Math. Biol. 60: 247-273.
11. Crutchfield, J. P., Farmer, J. D. and Huberman, B. A. 1982. Fluctuations and simple chaotic dynamics. - Phys. Rep. 92: 45-82.
12. Cushing, J. M., Dennis, B., Desharnais, R. A. and Costantino, R. F. 1996. An interdisciplinary approach to understanding nonlinear ecological dynamics. - Ecol. Model. 92: 111-119.
13. Cushing, J. M., Dennis, B., Desharnais, R. A. and Costantino, R. F. 1998a. Moving toward an unstable equilibrium: saddle nodes in population systems. - J. Anim. Ecol. 67: 298-306.
14. Cushing, J. M., Costantino, R. F., Dennis, B. et al. 1998b. Nonlinear population dynamics: models, experiments, and data. - J. Theor. Biol. 194: 1-9.
15. Cushing, J. M., Henson, S. M., Desharnais, R. A. et al. 2001. A chaotic attractor in ecology: theory and experimental data. - Chaos Sol. Fract. 12: 219-234.
16. Dennis, B. and Patil, G. P. 1984. The gamma distribution and weighted multimodal gamma distributions as models of population abundance. - Math. Biosciences 68: 187-212.
17. Dennis, B. and Costantino, R. F. 1988. Analysis of steady-state distributions with the gamma abundance model: application to Tribolium. - Ecology 69: 1200-1213.
18. Dennis, B., Munholland, P. L. and Scott, J. M. 1991. Estimation of growth and extinction parameters for endangered species. - Ecol. Monogr. 61: 115-143.
19. Dennis, B., Desharnais, R. A., Cushing, J. M. and Costantino, R. F. 1995. Nonlinear demographic dynamics: mathematical models, statistical methods, and biological experiments. - Ecol. Monogr. 65: 261-281.
20. Dennis, B., Desharnais, R. A., Cushing, J. M. and Costantino, R. F. 1997. Transitions in population dynamics: equilibria to periodic cycles to aperiodic cycles. - J. Anim. Ecol. 66: 704-729.
21. Dennis, B., Desharnais, R. A., Cushing, J. M. et al. 2001. Estimating chaos and complex dynamics in an insect population. - Ecol. Monogr. 71: 277-303.
22. Desharnais, R. A., Dennis, B. and Costantino, R. F. 1990. Genetic analysis of a population of Tribolium. IX. Maximization of population size and the concept of a stochastic equilibrium. - Genome 33: 571-580.
23. Desharnais, R. A., Costantino, R. F., Cushing, J. M. and Dennis, B. 1997. Estimating chaos in an insect population. - Science 276: 1881-1882.
24. Desharnais, R. A., Costantino, R. F., Cushing, J. M. et al. 2001. Chaos and population control of insect outbreaks. - Ecol. Lett. 4: 229-235.
25. Drazin, P. G. 1992. Nonlinear systems. - Cambridge Univ. Press.
26. Eckmann, J.-P. and Ruelle, D. 1985. Ergodic theory of chaos and strange attractors. - Rev. Mod. Phys. 57: 617-656.
27. Ellner, S. and Turchin, P. 1995. Chaos in a noisy world: new methods and evidence from time series analysis. - Am. Nat. 145: 343-375.
28. Ellner, S., Gallant, A. R., McCaffrey, D. and Nychka, D. 1991. Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data. - Phys. Lett. A 153: 357-363.
29. Falck, W., Bjørnstad, O. N. and Stenseth, N. C. 1995a. Bootstrap estimated uncertainty of the dominant Liapunov exponent for the Holarctic microtine rodents. - Proc. R. Soc. Lond. B 261: 159-165.
30. Falck, W., Bjørnstad, O. N. and Stenseth, N. C. 1995b. Voles and lemmings: chaos and uncertainty in fluctuating populations. - Proc. R. Soc. Lond. B 262: 363-370.
31. Gao, J. B., Hwang, S. K. and Liu, J. M. 1999. When can noise induce chaos. - Phys. Rev. Lett. 82: 1132-1136.
32. Gardiner, C. W. 1983. Handbook of stochastic methods for physics, chemistry, and the natural sciences. - Springer-Verlag.
33. Gotelli, N. J. 1995. A primer of ecology. - Sinauer Associates.
34. Grenfell, B. T., Bjømstad, O. N. and Finkenstädt, B. 2002. Endemic and epidemic dynamics of measles, II. Scaling predictability, noise and determinism with the time-series SIR model. - Ecol. Monogr. 72: 185-202.
35. Hassell, M. P., Lawton, J. H. and May, R. M. 1976. Patterns of dynamical behavior in single species populations. - J. Anim. Ecol. 45: 471-486.
36. Hastings, A. 1997. Population biology: concepts and models. - Springer-Verlag.
37. Hastings, A., Hom, C. L., Ellner, S. et al. 1993. Chaos in ecology: is mother nature a strange attractor. - Annu. Rev. Ecol. Systemat. 24: 1-33.
38. Henson, S. M., Costantino, R. F., Cushing, J. M. et al. 1999. Multiple attractors, saddles, and population dynamics in periodic habitats. - Bull. Math. Biol. 61: 1121-1149.
39. Henson, S. M., Costantino, R. F., Cushing, J. M. et al. 2001. Lattice effects observed in chaotic dynamics of experimental populations. - Science 294: 602-605.
40. Horsthemke, W. and Lefever, R. 1984. Noise-induced transitions. - Springer-Verlag.
41. Karlin, S. and Taylor, H. M. 1981. A second course in stochastic processes. - Academic Press.
42. Kemp, W. P. and Dennis, B. 1993. Density dependence and rangeland grasshoppers (Orthoptera: Acrididae). - Oecologia 96: 1-8.
43. Kingsland, S. E. 1985. Modeling nature: episodes in the history of population ecology. - Univ. of Chicago Press.
44. Kolata, G. 1986. What does it mean to be random. - Science 231: 1068-1070.
45. Lande, R. and Orzack, S. H. 1988. Extinction dynamics of age-structured populations in a fluctuating environment. - Proc. Natl. Acad. Sci. USA 85: 7418-7421.
46. Lasota, A. and Mackey, M. C. 1985, Probabilistic properties of deterministic systems. - Cambridge Univ. Press.
47. Leigh, E. G. 1968. The ecological role of Volterra's equations. - In: Gerstenhaber, M. (ed.), Some mathematical problems in biology. Am. Math. Soc., pp. 1-61.
48. Leigh, E. G. 1981. The average lifetime of a population in a varying environment. - J. Theor. Biol. 90: 213-239.
49. May, R. M. 1974a. Stability and complexity in model ecosystems, second edition. - Princeton Univ. Press.
50. May, R. M. 1974b. Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. - Science 186: 645-647.
51. May, R. M. (ed.) 1976. Theoretical ecology: principles and applications. - W. B. Saunders.
52. May, R. M. 1986. When two and two do not make four: nonlinear phenomena in ecology. - Proc. R. Soc. Lond. B 228: 241-266.
53. May, R. M. and Oster, G. F. 1976. Bifurcations and dynamic complexity in simple ecological models. - Am. Nat. 110: 573-599.
54. Mayer-Kress, G. and Haken, H. 1981. The influence of noise on the logistic model. - J. Stat. Phys. 26: 149-171.
55. McCaffrey, D. F., Ellner, S., Gallant, A. R. and Nychka, D. W. 1992. Estimating the Lyapunov exponent of a chaotic system with nonparametric regression. - J. Am. Statist. Assoc. 87: 682-695.
56. Nychka, D., Ellner, S., McCaffrey, D. and Gallant, A. R. 1992. Finding chaos in noisy systems. - J. R. Statist. Soc. B 54: 399-426.
57. Perry, J. N., Woiwod, I. P., Smith, R. H. and Morse, D. 1997. Estimating chaos in an insect population. - Science 276: 1881-1882.
58. Poole, R. 1989a. Is it chaos, or is it just noise. - Science 243: 25-28.
59. Poole, R. 1989b. Ecologists flirt with chaos. - Science 243: 310-313.
60. Rand, D. A. and Wilson, H. B. 1991. Chaotic stochasticity: a ubiquitous source of unpredictability in epidemics. - Proc. R. Soc. Lond. B 246: 179-184.
61. Rice, J. A. 1995. Mathematical statistics and data analysis, second edition. - Wadsworth.
62. Schaffer, W. M. 1985. Order and chaos in ecological systems. - Ecology 66: 93-106.
63. Scudo, F. M. and Ziegler, J. R. 1978. The golden age of theoretical ecology: 1923-1940. Lecture notes in biomathematics. Vol. 22. - Springer-Verlag.
64. Shaffer, M. L. 1981. Minimum population sizes for species conservation. - Bioscience 31: 131-134.
65. Tong, H. 1990. Nonlinear time series: a dynamical system approach. - Oxford Univ. Press.
66. Tong, H. 1996. Some comments on nonlinear time series analysis. - Fields Inst. Com. 11: 17-27.
67. Turchin, P. 1993. Chaos and stability in rodent population dynamics: evidence from nonlinear time-series analysis. - Oikos 68: 167-172.
68. Turchin, P. 1995. Chaos in microtine populations. - Proc. R. Soc. Lond. B 262: 357-361.
69. Turchin, P. 2003. Complex population dynamics: a theoretical/empirical synthesis. - Princeton Univ. Press.
70. Turchin, P. and Ellner, S. P. 2000. Living on the edge of chaos: population dynamics of Fennoscandian voles. - Ecology 81: 3099-3116.
71. Turchin, P. and Taylor, A. D. 1992. Complex dynamics in ecological time series. - Ecology 73: 289-305.
72. Yao, Q. and Tong, H. 1994. On prediction and chaos in stochastic systems. - Phil. Trans. R. Soc. Lond. A 348: 357-369.
73. West, B. J. 1985. An essay on the importance of being nonlinear. Lecture notes in biomathematics. Vol. 62. - Springer-Verlag.