ABSTRACT
We design and report an electrical circuit using a Josephson junction under periodic forcing that reveals extreme multistability. Its overall state equations surprisingly recall those of a well-known model of Josephson junction initially introduced in our circuit. The final circuit is characterized by the presence of two new and different current sources in parallel with the nonlinear internal current source sin[Ï(t)] of the Josephson junction single electronic component. Furthermore, the model presents an interesting extreme multistability which is justified by a very large number of different attractors (chaotic or not) when slightly changing the initial conditions.
ABSTRACT
This paper 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. Both mathematical investigations and numerical simulations followed by pspice experiment are presented to show the feasibility of the proposed method.
