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Chaos resulting from nonlinear relations between different variables

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  • Dohtani, Akitaka

Abstract

In this study, we further develop the perturbation method of Marotto [6] and investigate the general mechanisms responsible for nonlinear dynamics, which are typical of multidimensional systems. We focus on the composites of interdependent relations between different variables. First, we prove a general result on chaos, which shows that the cyclic composites of nonlinear interdependent relations are sources of chaotic dynamics in multidimensional systems. By considering several examples, we conclude that the cyclic composites play an important role in detecting chaotic dynamics.

Suggested Citation

  • Dohtani, Akitaka, 2011. "Chaos resulting from nonlinear relations between different variables," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 290-297.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:4:p:290-297
    DOI: 10.1016/j.chaos.2011.02.004
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    1. Marotto, F.R., 2005. "On redefining a snap-back repeller," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 25-28.
    2. Gaertner, Wulf & Jungeilges, Jochen, 1988. "A non-linear model of interdependent consumer behaviour," Economics Letters, Elsevier, vol. 27(2), pages 145-150.
    3. Jess Benhabib & Richard H. Day, 1981. "Rational Choice and Erratic Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(3), pages 459-471.
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