Mikhail M. Sushchik

Performance analysis of correlation-based communication schemes utilizing chaos

Using chaotic signals in spread-spectrum communications has a few clear advantages over traditional approaches. Chaotic signals are nonperiodic, wideband, and more difficult to predict, reconstruct, and characterize than periodic carriers. These properties of chaotic signals make it more difficult to intercept and decode the information modulated upon them. However, many suggested chaos-based communication schemes do not provide processing gain, a feature highly desirable in spread-spectrum communication schemes. In this paper, we suggest two communication schemes that provide a processing gain. The performance of these and of the earlier proposed differential chaos shift keying is studied analytically and numerically for discrete time implementations. It is shown that, when performance is characterized by the dependence of bit error rate on E/sub b//N/sub 0/, the increase of the spreading sequence length beyond a certain point degrades the performance. For a given E/sub b//N/sub 0/, there is a length of the spreading sequence that minimizes the bit error rate.

Chaotic pulse position modulation: a robust method of communicating with chaos

In this letter we investigate a communication strategy for digital ultra-wide bandwidth impulse radio, where the separation between the adjacent pulses is chaotic arising from a dynamical system with irregular behavior. A pulse position method is used to modulate binary information onto the carrier. The receiver is synchronized to the chaotic pulse train, thus providing the time reference for information extraction. We characterize the performance of this scheme in terms of error probability versus E/sub b//N/sub 0/ by numerically simulating its operation in the presence of noise and filtering.

Multiplexing chaotic signals using synchronization

Abstract Chaotic synchronization usually involves two coupled chaotic systems, with either one driving the other, or both being mutually coupled. In this paper we address a problem of synchronizing more than one pair of chaotic systems using only one communication channel. We demonstrate the principal possibility of multiplexing chaotic signals using synchronization both for iterated maps and ordinary differential equations. Possible applications for communication purposes are discussed.

The Eckhaus instability in hexagonal patterns

Abstract The Eckhaus instability of hexagonal patterns is studied within the model of three coupled envelope equations for the underlying roll systems. The regions of instability in the parameter space are found analytically from both the phase approximation and a full system of amplitude equations. Beyond the stability limits of hexagons two different modes go unstable. Both provide symmetry breaking of an initially regular pattern via splitting of a triplet of rolls into two triplets of growing disturbances. The parameters of fastest growing disturbances (wavelength, orientation, growth rate) are determined from the full set of linearized amplitude equations. The nonlinear stage of the Eckhaus instability is investigated numerically. Symmetry breaking due to the Eckhaus instability indeed occurs within a certain range of parameters, which for small supercriticality parameter μ leads to a metastable disordered hexagonal state with numerous line and point defects. For larger μ the Eckhaus instability triggers the transition of regular hexagonal pattern to disordered roll state. The roll phase originates in the cores of defects and then spreads all over the pattern.

Robustness and stability of synchronized chaos: an illustrative model

Synchronization of two chaotic systems is not guaranteed by having only negative conditional or transverse Lyapunov exponents. If there are transversally unstable periodic orbits or fixed points embedded in the chaotic set of synchronized motions, the presence of even very small disturbances from noise or inaccuracies from parameter mismatch can cause synchronization to break down and lead to substantial amplitude excursions from the synchronized state. Using an example of coupled one dimensional chaotic maps we discuss the conditions required for robust synchronization and study a mechanism that is responsible for the failure of negative conditional Lyapunov exponents to determine the conditions for robust synchronization.

Patterns in networks of oscillators formed via synchronization and oscillator death

Pattern formation via synchronization and oscillator death is considered in networks of diffusively coupled limit-cycle oscillators. Different examples of patterns and their dynamics are presented including nontrivial effects such as: (i) synchronized clusters induced by disorder and (ii) transitions from non-propagation to propagation of fronts via the intermittency.

Experimental observation of synchronized chaos with frequency ratio 1 : 2

The results of the experimental observation of synchronized chaos in circuits generating chaotic oscillations with different characteristic frequencies are presented. This synchronized chaotic behavior is studied in a system composed of an autonomous chaotic driving circuit and a response circuit. Onset of synchronization is detected by the auxiliary system method.

Observation of chaotic instability in the active mode locking of a semiconductor laser

We examine experimentally the consequence of frequency detuning an actively mode-locked external-cavity semiconductor laser from resonance. We observe a transition of the laser system from a periodic oscillation to a nonperiodic state with broadened spectral tones. By estimating the fractal dimension of the corresponding phase-space attractors, we show the presence of low-dimensional chaos. The route to chaos is a well-defined regime of three-frequency quasi-periodicity preceded by a two-frequency quasi-periodicity.

LOCAL OR DYNAMICAL DIMENSIONS OF NONLINEAR SYSTEMS INFERRED FROM OBSERVATIONS

In time delay reconstruction of the phase space of a system from observed scalar data, one requires a time lag and an integer embedding dimension. The minimum embedding dimension, dE, may be larger than the actual local dimension of the underlying dynamics, dL. The embedding theorem only guarantees that the attractor of the system is unfolded in the integer dE greater than 2dA with dA being the attractor dimension. We present two methods for determining the dimension, dL≤dE, of the underlying dynamics. The first relies on the local Lyapunov exponents of the dynamics, and the second seeks an optimum dimension for prediction of the time series for steps forward and then backward in time. We demonstrate these methods on several examples. Model building of the dynamics should take place in the dL-dimensional space.

Coherent structures in coupled chains of self-excited oscillators

Abstract Oscillations in a system of two coupled chains of identical limit-cycle oscillators are investigated. It is shown that a pair of coupled chains with different collective frequencies exhibits stable fronts between two possible asymptotic states. The inhomogeneous states formed by the fronts persist for weak coupling between the oscillators in each chain due to the discrete space variable, thus providing conditions for the existence of localized structures. For stronger coupling, the interface between two regions of the chains may propagate. The mean speed of propagation is investigated numerically and the results are compared with qualitative analysis.