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Summary
This summary is machine-generated.

Adding a perturbation to chaotic models like the Ricker map can reverse period doubling, leading to a stable two-cycle. This behavior differs in spatial models, where cell dynamics may not mirror the overall map.

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Area of Science:

  • Dynamical systems
  • Nonlinear dynamics
  • Chaos theory

Background:

  • The Ricker and logistic maps commonly exhibit a period-doubling route to chaos as the growth rate increases.
  • This route is typically irreversible in standard models.

Purpose of the Study:

  • To investigate the effect of constant positive perturbations on the period-doubling route to chaos in discrete dynamical systems.
  • To explore whether similar behaviors are observed in discrete spatial models derived from scalar maps.

Main Methods:

  • Analysis of the Ricker and logistic maps under constant positive perturbations.
  • Examination of discrete spatial models where cell values depend on nearest neighbors.
  • Comparison of dynamics in scalar maps versus their spatial generalizations.

Main Results:

  • The Ricker model, unlike the logistic map, shows period doubling reversals and a return to a stable two-cycle upon perturbation.
  • Several other maps exhibiting similar perturbation-induced reversals are identified.
  • Spatial generalizations of these maps do not necessarily display a uniform 2-cycle behavior across all cells, even when the scalar map achieves a stable 2-cycle.

Conclusions:

  • Constant positive perturbations can introduce novel dynamics, including reversals of chaos, in certain discrete maps.
  • The transition to chaos and its reversal are sensitive to model structure, particularly in spatial extensions.
  • Predicting the behavior of discrete spatial models based solely on their scalar map counterparts is not always feasible.