Implications of semi-stable attractors for ecological modelling

Ecological Modelling

Volumn 89, Issue 1-3, 1996, Pages 59-65

  Byers, R E ^a   Hansell, R I C ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Dynamical systems; Stability

Indexed keywords

AGE-STRUCTURED MODEL; DYNAMIC SYSTEM; MODELLING; SEMI-STABLE ATTRACTOR;

EID: 0030500435     PISSN: 03043800     EISSN: None     Source Type: Journal    
DOI: 10.1016/0304-3800(95)00120-4     Document Type: Article

References (14)

1. Battelino, P.M., Grebogi, C., Ott, E., Yorke, J.A. and Yorke, E.D., 1988. Multiple coexisting attractors, basin boundaries and basic sets, Physica D, 32: 296-305.
2. Byers, R.E., Hansell, R.I.C. and Madras, N., 1989. Complex behavior of systems due to semi-stable attractors: attractors that have been destablized but which still temporarily dominate the dynamics of a system. In: N.B. Abraham, A.M. Albano, A. Passamante and P.E. Rapp (Editors), Measures of Complexity and Chaos. Nato ASI series, Series B: Physics Vol. 208. Plenum Press, New York in cooperation with NATO Scientific Affairs Division, pp. 219-223.
3. Byers, R.E., Hansell, R.I.C. and Madras, N., 1992. Stability-like properties of population models. Theor. Popul. Biol., 42: 10-34.
4. Carroll, T.L., Pecora, L.M. and Rachford, F.J., 1987a. Chaotic transients and multiple attractors in spin-wave experiments. Phys. Rev. Let., 59: 2891-2894.
5. Carroll, T.L., Rachford, F.J. and Pecora, L.M., 1987b. Occurrence of chaotic transients during transitions between quasiperiodic states in yttrium iron garnet. Phys. Rev. B, 38: 2938-2940.
6. Feller, W., 1971. An Introduction to Probability Theory and its Applications, second edition. John Wiley and Sons, New York, 669 pp.
7. Fisher, R.A., Corbet, A.S. and Williams, C.B., 1943. The relation between the number of species and the number of individuals in a random sample of an animal population, J. Anim. Ecol., 12: 42-57.
8. Grebogi, C., Ott, E. and Yorke, J.A., 1986. Critical exponent of chaotic transients in nonlinear dynamical systems, Phys. Rev. Let., 57: 1284-1287.
9. Karlin, S. and McGregor, J., 1967. The number of mutant forms maintained in a population. Proceedings of the fifth Berkeley Symposium, Math. Stat. Prob., 4: 415-438.
10. Karlin, S. and McGregor, J., 1972. Addendum to a paper of W. Ewens. Theor. Popul. Biol., 3: 113-117.
11. Livi, R., Martinez-Mekler, G. and Rufo, S., 1990. Periodic orbits and long transients in coupled map lattices. Physica D, 45: 452-460.
12. McCann, K. and Yodzis, P., 1994. Nonlinear dynamics and population disappearances, Am. Nat., 144: 873-879.
13. Simon, H.A., 1955. On a class of skew distribution functions. Biometrika, 42: 425-440.
14. Williams, C.B., 1964. Patterns in the Balance of Nature. Academic Press, New York, 324 pp.