Chaos resulting from nonlinear relations between different variables

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Copyright © 2011 Elsevier Ltd All rights reserved.The definitive version is published in Chaos, Solitons & Fractals Volume 44, Issue 4-5, March 2011, doi:10.1016/j.chaos.2011.02.004In this study, we further develop the perturbation method of Marotto (1979)and investigate the general mechanisms responsible for nonlinear dynamics, which aretypical of multidimensional systems. We focus on the composites of interdependentrelations between different variables. First, we prove a general result on chaos, whichshows that the cyclic composites of nonlinear interdependent relations are sources ofchaotic dynamics in multidimensional systems. By considering several examples, weconclude that the cyclic composites play an important role in detecting chaoticdynamics.