Finite-time synchronization of tunnel diode based chaotic oscillators

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 simulatioComment: 11 pages, 43 figure

Complex Dynamics and Synchronization of Delayed-Feedback Nonlinear Oscillators

We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital-signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions under which they will synchronize. By examining the rates of divergence or convergence between two coupled oscillators, we quantify the maximum Lyapunov exponents or transverse Lyapunov exponents of the system, and we present an experimental method to determine these rates that does not require a mathematical model of the system. Finally, we demonstrate a new adaptive control method that keeps two oscillators synchronized even when the coupling between them is changing unpredictably.Comment: 24 pages, 13 figures. To appear in Phil. Trans. R. Soc. A (special theme issue to accompany 2009 International Workshop on Delayed Complex Systems

Time Scaling of Chaotic Systems: Application to Secure Communications

The paper deals with time-scaling transformations of dynamical systems. Such scaling functions operate a change of coordinates on the time axis of the system trajectories preserving its phase portrait. Exploiting this property, a chaos encryption technique to transmit a binary signal through an analog channel is proposed. The scheme is based on a suitable time-scaling function which plays the role of a private key. The encoded transmitted signal is proved to resist known decryption attacks offering a secure and reliable communication.Comment: 15 pages, 7 figure

On-Off Intermittency in Time Series of Spontaneous Paroxysmal Activity in Rats with Genetic Absence Epilepsy

Dynamic behavior of complex neuronal ensembles is a topic comprising a streamline of current researches worldwide. In this article we study the behavior manifested by epileptic brain, in the case of spontaneous non-convulsive paroxysmal activity. For this purpose we analyzed archived long-term recording of paroxysmal activity in animals genetically susceptible to absence epilepsy, namely WAG/Rij rats. We first report that the brain activity alternated between normal states and epilepsy paroxysms is the on-off intermittency phenomenon which has been observed and studied earlier in the different nonlinear systems.Comment: 11 pages, 6 figure

Chaotic Free-Space Laser Communication over Turbulent Channel

The dynamics of errors caused by atmospheric turbulence in a self-synchronizing chaos based communication system that stably transmits information over a $\sim$5 km free-space laser link is studied experimentally. Binary information is transmitted using a chaotic sequence of short-term pulses as carrier. The information signal slightly shifts the chaotic time position of each pulse depending on the information bit. We report the results of an experimental analysis of the atmospheric turbulence in the channel and the impact of turbulence on the Bit-Error-Rate (BER) performance of this chaos based communication system.Comment: 4 pages, 5 figure