Research Article Open Access

The Possibility of Cyclical Behavior in a Class of Dynamic Models

Anjan Mukherji1
  • 1 ,
American Journal of Applied Sciences
Volume 2 No. 13, 2005, 27-38

DOI: https://doi.org/10.3844/ajassp.2005.27.38

Published On: 9 December 2005

How to Cite: Mukherji, A. (2005). The Possibility of Cyclical Behavior in a Class of Dynamic Models. American Journal of Applied Sciences, 2(13), 27-38. https://doi.org/10.3844/ajassp.2005.27.38

Abstract

The study investigates conditions under which endogenous cyclic behavior may be observed within the context of Predator-Prey (Lotka-Volterra) Models. The analysis also establishes conditions under which such behavior is non-existent and hence establishes conditions for global convergence to the interior equilibrium, whenever it exists. The results are then applied to two diverse sets of economic exercises and shows how the conclusions of those exercises may be established under a much weaker set of assumptions. Based on these discussions, a numerical example of robust periodic behavior is provided.

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Keywords

  • Predator-prey models
  • Lotka-Volterra models
  • robust periodic behavior
  • Dulac’s criterion
  • Poincaré-Bendixson theorem
  • Goodwin growth model
  • Easter Island mystery