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Dynamics Of Physical Systems By Discrete Time Coupling

Luis Javier Ontañón, Eric Campos Canton
We present here an example of how to synchronize physical systems inspired in biological models using the Poincare coupling. With this type of coupling one is able to study the synchronization phenomena among coupled systems by means of a detection of a threshold without disrupting the monitored system. The idea is to generate a coupling signal, triggered in discrete periods of time as a response to the crossing events of the monitored systems orbit with the previously defined Poincare plane. This type of coupling comes to satisfy the needs of forcing a system for some specific intervals of time, for example periodic, chaotic or random events of triggering. In order to detect if the systems are synchronized we use two methods: i) the auxiliary system
method measuring the Euclidean distance among the forced systems, ii) the maximum conditional Lyapunov exponent. An illustrative example is given by computer simulations in order to demonstrate the approach proposed.
CYBERNETICS AND PHYSICS, Vol. 2, No. 4, 217–221.
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