Bifurcations and synchronization using an integrated programmable chaotic circuit

This paper presents a CMOS chip which can act as an autonomous stand-alone unit to generate different real-time chaotic behaviors by changing a few external bias currents. In particular, by changing one of these bias currents, the chip provides different examples of a period-doubling route to chaos. We present experimental orbits and attractors, time waveforms and power spectra measured from the chip. By using two chip units, experiments on synchronization can be carried out as well in real-time. Measurements are presented for the following synchronization schemes: linear coupling, drive-response and inverse system. Experimental statistical characterizations associated to these schemes are also presented. We also outline the possible use of the chip for chaotic encryption of audio signals. Finally, for completeness, the paper includes also a brief description of the chip design procedure and its internal circuitry

Nonlinear Dynamics of Chaotic Attractor of Chua Circuit and Its Application for Secure Communication

The Chua circuit is among the simplest non-linear circuits that shows most complex dynamical behavior, including chaos which exhibits a variety of bifurcation phenomena and attractors. In this paper, Chua attractor's chaotic oscillator, synchronization and masking communication circuits were designed and simulated. The electronic circuit oscilloscope outputs of the realized Chua system is also presented. Simulation and oscilloscope outputs are used to illustrate the accuracy of the designed and realized Chua chaotic oscillator circuits. The Chua system is addressed suitable for chaotic synchronization circuits and chaotic masking communication circuits using Matlab® and MultiSIM® software. Simulation results are used to visualize and illustrate the effectiveness of Chua chaotic system in synchronization and application of secure communication.  Keywords: chua nonlinear circuit, chaotic attractor, chaotic synchronization, secure communication

Spread spectrum modulation and signal masking using synchronized chaotic systems

Includes bibliographical references (leaves 36-37).Research supported in part by the Air Force Office of Scientific Research. AFOSR-91-0034-A Research supported in part by Lockheed Sanders, Inc., under the U.S. Navy Office of Naval Research. N00014-91-C-0125Kevin M. Cuomo, Alan V. Oppenheim, and Steven H. Isabelle

An alternative solution to the model structure selection problem

An alternative solution to the model structure selection problem is introduced by conducting a forward search through the many possible candidate model terms initially and then performing an exhaustive all subset model selection on the resulting model. An example is included to demonstrate that this approach leads to dynamically valid nonlinear model

One mechanism of appearance of a spiral quasiattractor involving heteroclinic contours

AbstractBifurcations and the structure of limit sets are studied for a three-dimensional van der Pol-Duffing system with a cubic nonlinearity. On a base of both computer simulations and theoretical results a model map is proposed which allows one to follow the evolution in the phase space from a simple (Morse-Smale) structure to chaos. It is established that appearance of complex, multistructural set of double-scroll type is stipulated by the presence of a heteroclinic orbit of intersection of the unstable manifold of a saddle periodic orbit and stable manifold of an equilibrium state of saddle-focus type

Topics in chaotic secure communication

Results in nonlinear dynamics and chaos during this decade have been applied to problems in secure communications with limited success. Most of these applications have been based on the chaotic synchronization property discovered by Pecora and Carroll in 1989 [37]. Short [44, 45, 48] demonstrated the effectiveness of nonlinear dynamic (NLD) forecasting methods in breaking this class of communication schemes. In response, investigators have proposed enhancements to the basic synchronization technique in an attempt to improve the security properties. In this work two of these newer communication systems will be analyzed using NLD forecasting and other techniques to determine the level of security they provide. It will be shown that the transmitted waveform alone allows an eavesdropper to extract the message. During the course of this research, a new impulsively initialized, binary chaotic communication scheme has been developed, which eliminates the most significant weaknesses of its predecessors. This new approach is based on symbolic dynamics and chaotic control, and may be implemented using one-dimensional maps, which gives the designer more control over the statistics of the transmitted binary stream. Recent results in a certain class of one-dimensional chaotic maps will be discussed in this context. The potential for using NLD techniques in problems from standard digital communications will also be explored. The two problems which will be addressed are bit errors due to channel effects and co-channel interference. It will be shown that NLD reconstruction methods provide a way to exploit the short-term determinism that is present in these types of communication signals

Nonlinear dynamic of the multicellular chopper

International audienceIn this paper, the dynamics of multicellular chopper are considered. The model is described by a continuous time three-dimensional autonomous system. Some basic dynamical properties such as Poincaré mapping, power spectrum and chaotic behaviors are studied. Analysis results show that this system has complex dynamics with some interesting characteristics