The possibility of chaos control in biological systems has been stimulated by recent advances in the study of heart and brain tissue dynamics. More recently, some authors have conjectured that such a method might be applied to population dynamics and even play a nontrivial evolutionary role in ecology. In this paper we explore this idea by means of both mathematical and individual-based simulation models. Because of the intrinsic noise linked to individual behavior, controlling a noisy system becomes more difficult but, as shown here, it is a feasible task allowed to be experimentally tested. c ○ 1999 Society for Mathematical Biology 1.
|
71
|
Simple mathematical models with very complicated dynamics
– May
- 1976
|
|
62
|
Controlling chaos
– Ott, Grebogi, et al.
- 1990
|
|
23
|
The rise of the individual-based model in ecology
– Judson
- 1994
|
|
18
|
Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos
– May
- 1974
|
|
16
|
Resolving Discrepancies between Deterministic Population Models and Individual-Based Simulations
– Wilson
- 1998
|
|
15
|
Controlling cardiac chaos
– Garfinkel, Spano, et al.
- 1992
|
|
14
|
The Balance of Nature
– Pimm
- 1991
|
|
13
|
Experimental control of chaos”, Phys
– Ditto, Rauseo, et al.
- 1990
|
|
13
|
Experimental control of chaos
– Ditto, Rauseo, et al.
- 1990
|
|
13
|
Bifurcations and dynamic complexity in simple ecological models Am
– MAY, OSTER
- 1976
|
|
11
|
Chaos in a three-species food chain
– Hastings, Powell
- 1991
|
|
11
|
Weak trophic interactions and the balance of nature. – Nature 395: 794–798
– McCann, Hastings, et al.
- 1998
|
|
8
|
Complex interactions between dispersal and dynamics: lessons from coupled logistic equations
– Hastings
- 1993
|
|
7
|
Multiple attractors, catastrophes an chaos in seasonally perturbed predator-prey communities
– Rinaldi, Muratori, et al.
|
|
6
|
Experimentally induced transitions in the dynamic behavior of insect populations, Nature 375
– Costantino, Cushing, et al.
- 1995
|
|
6
|
Chaotic dynamics in an insect population
– Costantino, Desharnais, et al.
- 1997
|
|
6
|
Complex dynamics in a model microbial system
– Kot, Sayler, et al.
- 1992
|
|
6
|
Controlling chaos in the brain
– Schiff, Jerger, et al.
- 1994
|
|
5
|
Chaos reduces species extinction by amplifying local population noise
– Allen, Schaffer, et al.
- 1993
|
|
4
|
Transitions in population dynamics: Equilibria to periodic cycles to aperiodic cycles
– Dennis, Desharnais, et al.
- 1997
|
|
4
|
Period-doubling reversals and chaos in simple ecological models
– Stone
- 1993
|
|
3
|
Should we expect strange attractors behind plankton dynamics-and if so, should we bother
– Scheffer
- 1991
|
|
2
|
Controlling spatiotemporal chaos in a chain of coupled logistic maps
– Astakhov, Ansihehenko, et al.
- 1995
|
|
2
|
Rethinking complexity— modelling spatiotemporal dynamics in ecology. Trends Ecol
– Solé
- 1995
|
|
2
|
Complex dynamics in multispecies communities
– Godfray
- 1990
|
|
2
|
Avoiding chaos
– Lomnicki
- 1989
|
|
2
|
Avoiding chaos. Trends Ecol
– Nisbet, Blythe, et al.
- 1989
|
|
2
|
Properties of an aquatic microecosystem. II. Steady-state phenomena in the autotrophic subsystem
– Ringelberg
- 1977
|
|
2
|
Stretching and folding in lynx for returns: evidence for a strange attractor in nature
– Schaffer
- 1984
|
|
2
|
Chaos in ecological systems: the coals that Newcastle forgot
– Schaffer, Kot
- 1986
|
|
2
|
de la Prida
– Solé, Menéndez
- 1995
|
|
2
|
Oscillations and chaos in the dynamics of a perennial grass
– Tilman, Wedin
- 1991
|
|
1
|
Are ecological systems chaotic—and if not, why not? Trends Ecol
– Berryman, Millstein
- 1989
|
|
1
|
Solé et al
– V
|
|
1
|
The evolutionary advantage of controlled chaos
– Doebeli
- 1993
|
|
1
|
Controlling spatiotemporal chaos in metapopulations with long-range dispersal
– Doebeli, Ruxton
- 1997
|
|
1
|
Effect of molecular fluctuations on the description of chaos by microvariable equations
– Fox, Keitzer
- 1990
|
|
1
|
Control of chaos in uni-dimensional maps
– Güemez, Matías
- 1993
|
|
1
|
Patterns of dynamical behavior in single-species populations
– Hassell, Lawton, et al.
- 1976
|
|
1
|
Effects of inmigration on chaotic population dynamics
– McCallum
- 1992
|
|
1
|
Controlling chaos in unidimensional maps using constant feedback
– Parthasarathy, Sinha
- 1995
|
|
1
|
Intrinsic fluctuations in chaotic dynamics
– Peeters, Nicolis
- 1992
|
|
1
|
Controlling Chaos in Ecology 1207
– Petrov, Gáspár, et al.
- 1993
|
|
1
|
Chaos in a cup of flour. Trends Ecol
– Rohani, Earn
- 1997
|
|
1
|
Chaos, dispersal and extinction in coupled ecosystems
– Solé, Gamarra
- 1998
|
|
1
|
Nonlinear phenomena and chaos in a Monte Carlo simulated microbial ecosystem
– Solé, Valls
- 1992
|
