Shawn D. Pethel

Lag and anticipating synchronization without time-delay coupling

We describe a new method for achieving approximate lag and anticipating synchronization in unidirectionally coupled chaotic oscillators. The method uses a specific parameter mismatch between the drive and response that is a first-order approximation to true time-delay coupling. As a result, an adjustable lag or anticipation effect can be achieved without the need for a variable delay line, making the method simpler and more economical to implement in many physical systems. We present a stability analysis, demonstrate the method numerically, and report experimental observation of the effect in radio-frequency electronic oscillators. In the circuit experiments, both lag and anticipation are controlled by tuning a single capacitor in the response oscillator.

High-precision ranging using a chaotic laser pulse train

We demonstrate the use of a chaotic laser pulse train for high-precision ranging. The pulse train is produced by inducing coherence collapse in an AlGaAs semiconductor laser. Measurements of optical spectra, intensity autocorrelation functions, and ladar ranging are presented.

Control of long-period orbits and arbitrary trajectories in chaotic systems using dynamic limiting

We demonstrate experimental control of long-period orbits and arbitrary chaotic trajectories using a new chaos control technique called dynamic limiting. Based on limiter control, dynamic limiting uses a predetermined sequence of limiter levels applied to the chaotic system to stabilize natural states of the system. The limiter sequence is clocked by the natural return time of the chaotic system such that the oscillator sees a new limiter level for each peak return. We demonstrate control of period-8 and period-34 unstable periodic orbits in a low-frequency circuit and provide evidence that the control perturbations are minimal. We also demonstrate control of an arbitrary waveform by replaying a sequence captured from the uncontrolled oscillator, achieving a form of delayed self-synchronization. Finally, we discuss the use of dynamic limiting for high-frequency chaos communications. (c) 2002 American Institute of Physics.

Transfer Entropy for Coupled Autoregressive Processes

A method is shown for computing transfer entropy over multiple time lags for coupled autoregressive processes using formulas for the differential entropy of multivariate Gaussian processes. Two examples are provided: (1) a first-order filtered noise process whose state is measured with additive noise, and (2) two first-order coupled processes each of which is driven by white process noise. We found that, for the first example, increasing the first-order AR coefficient while keeping the correlation coefficient between filtered and measured process fixed, transfer entropy increased since the entropy of the measured process was itself increased. For the second example, the minimum correlation coefficient occurs when the process noise variances match. It was seen that matching of these variances results in minimum information flow, expressed as the sum of transfer entropies in both directions. Without a match, the transfer entropy is larger in the direction away from the process having the larger process noise. Fixing the process noise variances, transfer entropies in both directions increase with the coupling strength. Finally, we note that the method can be generally employed to compute other information theoretic quantities as well.

A simple electronic system for demonstrating chaos control

In this note, we describe a simple electronic oscillator and controller for demonstrating chaos control. The oscillator is built using a LC tank circuit tuned near 1 kHz, and the controller is an active limiter. Both circuits can be constructed using common, inexpensive parts. As such, this system is well suited for laboratory demonstrations of chaos control, thereby providing students with valuable exposure to the emerging field of chaos engineering.

Exact Test of Independence Using Mutual Information

Using a recently discovered method for producing random symbol sequences with prescribed transition counts, we present an exact null hypothesis significance test (NHST) for mutual information between two random variables, the null hypothesis being that the mutual information is zero (i.e., independence). The exact tests reported in the literature assume that data samples for each variable are sequentially independent and identically distributed (iid). In general, time series data have dependencies (Markov structure) that violate this condition. The algorithm given in this paper is the first exact significance test of mutual information that takes into account the Markov structure. When the Markov order is not known or indefinite, an exact test is used to determine an effective Markov order.

Experimental targeting of chaos via controlled symbolic dynamics

In this Letter, we report experimental targeting in a chaotic system by controlling symbolic dynamics. We acquire and control an electronic circuit using small perturbations to elicit a desired objective state starting from an arbitrary, uncontrolled state. The control perturbations are calculated using a symbolic targeting sequence and applied using dynamic limiting control.

Limiter Control of a Chaotic RF Transistor Oscillator

We report experimental control of chaos in an electronic circuit at 43.9 MHz, which is the fastest chaos control reported in the literature to date. Limiter control is used to stabilize a periodic orbit in a tuned collector transistor oscillator modified to exhibit simply folded band chaos. The limiter is implemented using a transistor to enable monitoring the relative magnitude of the control perturbation. A plot of the relative control magnitude versus limiter level shows a local minimum at period-1 control, thereby providing strong evidence that the controlled state is an unstable periodic orbit (UPO) of the uncontrolled system.

Beam Steering by Lag Synchronization in Wide‐Bandwidth, Chaotic Arrays

Chaotic oscillators are an intriguing source of waveforms for ultra wideband‐radar applications. The broadband and nonrepeating nature of chaos provides an ideal combination of high range resolution and no range ambiguity. In addition, synchronization via local coupling of array elements is an efficient alternative to the use of a master oscillator in a phased array. However, a difficulty in any wideband array is achieving a practical mechanism for beam steering. Conventional approaches using phase shifters are impractical for bandwidths exceeding just a few percent of the carrier frequency, and for larger bandwidths true time‐delay steering is required. Here, we explore the use of lag synchronization in a chaotic array to achieve steering. The natural frequency of each oscillator is adjusted using a variable capacitor to achieve a uniform lag across the array. To first order this tuning is equivalent to a standard method of inducing lag synchronization. The direction and extent of the steering is directl...

Chaotic scrambling for wireless analog video

We report the implementation of a novel in-band chaotic scrambler for securing wireless analog video. In this demonstration system, an analog video signal is injected into a chaotic oscillator and the output is transmitted through a standard wireless radio link. At the receiver, a descrambler separates the video from the chaotic signal in real time. Experimental results show the scrambled signal effectively hides the original video image, yet the descrambler recovers the original color video with reasonable clarity and detail. Compared to digital encryption, chaotic scrambling offers an efficient, low-cost alternative for masking time-critical analog communications.