An approach for characterizing coupling in dynamical systems |
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Authors: | S Janjarasjitt KA Loparo |
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Institution: | aUbon Ratchathani University, Department of Electrical and Electronic Engineering, Warinchamrab, Ubon Ratchathani 34190, Thailand;bCase Western Reserve University, Department of Electrical Engineering and Computer Science, Cleveland, OH 44106, USA |
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Abstract: | The study of coupling in dynamical systems dates back to Christian Hyugens who, in 1665, discovered that pendulum clocks with the same length pendulum synchronize when they are near to each other. In that case the observed synchronous motion was out of phase. In this paper we propose a new approach for measuring the degree of coupling and synchronization of a dynamical system consisting of interacting subsystems. The measure is based on quantifying the active degrees of freedom (e.g. correlation dimension) of the coupled system and the constituent subsystems. The time-delay embedding scheme is extended to coupled systems and used for attractor reconstruction of the coupled dynamical system. We use the coupled Lorenz, Rossler and Hénon model systems with a coupling strength variable for evaluation of the proposed approach. Results show that we can measure the active degrees of freedom of the coupled dynamical systems and can quantify and distinguish the degree of synchronization or coupling in each of the dynamical systems studied. Furthermore, using this approach the direction of coupling can be determined. |
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Keywords: | Coupling Chaotic systems Nonlinear dynamics Time-delay embedding State space |
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