Interactions between Dispersal and Dynamics: Coupled Ricker's Equations
We study a one patch model using Ricker's equation, xn-1 = xner-xn, r ≥ 0. We reproduce some results that Hastings (1993) obtained by coupling two discrete time logistic equations. Multiple attractors could occur with dispersion where there is only one attractor without dispersion. The boundary of the basins of attraction of the attractors can be fractal in nature. This makes prediction of the asymptotic behavior of most initial conditions difficult to analyze. Furthermore, we study the same model using Ricker's equation. We show that the qualitative nature of the results for a system of difference equations with dispersion depends on the form of the local dynamics.
Eratóstenes Flores Torres, Universidad Nacional Autónoma de México