Abstract
Oscillations and chaos can be modelled and observed in a realistic simulation model of interacting prey-predator populations based on Monte Carlo simulation methods. These nonlinear phenomena are linked with some biological and physical bifurcation parameters and mathematical tools from dynamical systems theory may be used in order to characterize this behaviour. Chaotic dynamics are therefore, in our simulation, more the rule than the exception, and are related to delays associated with spatial degrees of freedom.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Giró, A., J. M. González, J. A. Padró and V. Torra. 1980. The structure of liquid lead at 760 K through molecular dynamics.J. Chem. Phys. 73, 2970–2972.
Giró, A., J. A. Padró, J. Valls and J. Wagensberg. 1985. Monte Carlo simulation of an ecosystem: a matching between two levels of observation.Bull. math. Biol. 47, 111–112.
Giró, A., J. Valls, J. A. Padró and J. Wagensberg. 1986. Monte Carlo simulation program for ecosystems.CABIOS 2, 291–296.
Godfray, H. C. and S. P. Blythe. 1990. Complex dynamics in multispecies communities.Phil. Trans. R. Soc. Lond. B330, 221–233.
Grassberger, P. and I. Procaccia. 1983. On the characterization of strange attractors.Phys. Rev. Lett. 50, 346–349.
Heerman, D. W. 1990.Computer Simulation Methods in Theoretical Physics. Berlin: Springer.
Hogeweg, P. and B. Hesper. 1990. Individual-oriented modelling in ecology.Math. Comp. Modelling 13, 83–90.
Huston, M. A., D. DeAngelis and W. Post. 1988. New computer models unify ecological theory.Bioscience 38, 682–691.
May, R. 1986. When two and two do not sum four: nonlinear phenomena in ecology.Proc. R. Soc. London B228, 241–257.
Mimura, M. and J. D. Murray. 1978. On a diffusive prey-predator model which exhibits patchiness.J. theor. Biol. 75, 249–262.
Parker, T. S. and L. O. Chua. 1989.Practical Numerical Algorithms for Chaotic Systems. Berlin: Springer.
Rössler, O. E. 1976. An equation for continuous chaos.Phys. Lett. 57A, 397–398.
Schaffer, W. M. 1984. Stretching and folding in lynx returns: evidence for a strange attractor in nature?Am. Nat. 124, 798–821.
Schaffer, W. M. and M. Kot. 1985. Do strange attractors govern ecological systems?Bioscience 35, 342–350.
Schuster, H. G. 1984.Deterministic Chaos. Weinheim: Physic-Verlag.
Solé, R. V. and J. Valls. 1990.Strange Attractors in Ecodynamics: Chaos in Monte Carlo Simulated Ecosystems. Modelling and Simulation. Proceedings of the 1990 European Simulation Multiconference, Nuremberg, pp. 624–629.
Solé, R. V. and J. Valls. 1991. Order and chaos in a 2D Lotka-Volterra coupled map lattice.Phys. Lett. A153, 330–336.
Solé, R. V. and J. Valls. 1992. On structural stability and chaos in biological systems.J. theor. Biol., in press.
Solé, R. V., D. López, M. Ginovart and J. Valls. 1992. Self-organized criticality in Monte Carlo simulated ecosystems.Phys. Lett. A, in press.
Takens, F. 1981.Lecture Notes in Physics, Vol. 898. Berlin: Springer.
Wagensberg, J., D. López and J. Valls. 1988. Statistical aspects of biological organization.J. Phys. Chem. Sol.,49, 695–700.
Wolf, A., J. B. Swift, H. L. Swinney and J. A. Vastano. 1985. Determining Lyapunov exponents from time series.Physica 16D, 285–317.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Solé, R.V., Valls, J. Nonlinear phenomena and chaos in a Monte Carlo simulated microbial ecosystem. Bltn Mathcal Biology 54, 939–955 (1992). https://doi.org/10.1007/BF02460660
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02460660