Complex discrete dynamics from simple continuous population models
Nonoverlapping generations have been classically modelled as difference equations in order to account for the discrete nature of reproductive events. However, other events such as resource consumption or mortality are continuous and take place in the within-generation time. We have realistically assumed a hybrid ODE bidimensional model of resources and consumers with discrete events for reproduction. Numerical and analytical approaches showed that the resulting dynamics resembles a Ricker map, including the doubling route to chaos. Stochastic simulations with a handling-time parameter for indirect competition of juveniles may affect the qualitative behaviour of the model.
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- Gurney, W. S. C. and R. M. Nisbet (1998). Ecological Dynamics, Oxford: Oxford University Press.Google Scholar
- Hassell, M. P., J. H. Lawton and R. M. May (1976). Patterns of dynamical behaviour in single species populations. J. Anim. Ecol. 45, 471–486.Google Scholar
- Mackey, M. C. and L. Glass (1977). Oscillations and chaos in physiological control systems. Science 197, 287–289.Google Scholar
- May, R. M. (1974). Biological populations with non-overlapping generations: stable points, stable cycles and chaos. Science 186, 645–647.Google Scholar
- Noy-Meir, I. (1979). Structure and function of desert ecosystems. Isr. J. Bot. 28, 1–9.Google Scholar
- Press, W. H., B. P. Flannery, S. A. Teukolsky and W. T. Vetterling (1993). Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd edn, Cambridge, UK: Cambridge University Press.Google Scholar
- Ricker, W. E. (1954). Stock and recruitment. J. Fish. Res. Bd. Can. 11, 559–623.Google Scholar