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.