Dynamics and indirect finite-time synchronization of chaotic systems

We addresses the problem of finite-time synchronization of tunnel
diode based chaotic oscillators.
After a brief investigation of its chaotic dynamics, we propose an
active adaptive feedback coupling which
accomplishes the synchronization of tunnel-diode-based chaotic
systems with and without the presence of
delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov
stability theories. This feedback coupling
could be applied to many other chaotic systems. A finite horizon
can
be arbitrarily established by ensuring that
chaos synchronization is achieved at a pre-established time. An
advantage of the proposed feedback coupling is
that it is simple and easy to implement. The case of relay-coupled
oscillators in a small network
of three chaotic oscillators will be discussed in detail