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Controlled Synchronization In Two Dynamical systems With Sector Bounded Nonlinearities

Sergei Plotnikov, Alexander Fradkov
We study synchronization in two delay-coupled
FitzHugh-Nagumo systems with slow-varying delays,
which are the simplest model of neural network. Further
we generalize FitzHugh-Nagumo model and consider
synchronization in the more common case. We
show that external stimulus can be used to control synchronization.
We develop one algorithm for synchronization
of FitzHugh-Nagumo systems and the other
one to control synchrony in the generalized neural
model, and find the conditions of their applicability.
The first algorithm provides synchronization in the
case, when all parameters are known and measurable,
while the second one is an adaptive controller and is
used in the case with uncertain parameters of the system.
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