William L. Ditto

Spatiotemporal evolution of ventricular fibrillation.

Sudden cardiac death is the leading cause of death in the industrialized world, with the majority of such tragedies being due to ventricular fibrillation. Ventricular fibrillation is a frenzied and irregular disturbance of the heart rhythm that quickly renders the heart incapable of sustaining life. Rotors, electrophysiological structures that emit rotating spiral waves, occur in several systems that all share with the heart the functional properties of excitability and refractoriness. These re-entrant waves, seen in numerical solutions of simplified models of cardiac tissue, may occur during ventricular tachycardias,. It has been difficult to detect such forms of re-entry in fibrillating mammalian ventricles. Here we show that, in isolated perfused dog hearts, high spatial and temporal resolution mapping of optical transmembrane potentials can easily detect transiently erupting rotors during the early phase of ventricular fibrillation. This activity is characterized by a relatively high spatiotemporal cross-correlation. During this early fibrillatory interval, frequent wavefront collisions and wavebreak generation are also dominant features. Interestingly, this spatiotemporal pattern undergoes an evolution to a less highly spatially correlated mechanism that lacks the epicardial manifestations of rotors despite continued myocardial perfusion.

Principles and applications of chaotic systems

There lies a behavior between rigid regularity and randomness based on pure chance. Its called a chaotic system, or chaos for short [5]. Chaos is all around us. Our notions of physical motion or dynamic systems have encompassed the precise clock-like ticking of periodic systems and the vagaries of dice-throwing chance, but have often been overlooked as a way to account for the more commonly observed chaotic behavior between these two extremes. When we see irregularity we cling to randomness and disorder for explanations. Why should this be so? Why is it that when the ubiquitous irregularity of engineering, physical, biological, and other systems are studied, it is assumed to be random and the whole vast machinery of probability and statistics is applied? Rather recently, however, we have begun to realize that the tools of chaos theory can be applied toward the understanding, manipulation, and control of a variety of systems, with many of the practical applications coming after 1990. To understand why this is true, one must start with a working knowledge of how chaotic systems behave—profoundly, but sometimes subtly different, from the behavior of random systems.

Techniques for the control of chaos

Abstract The concepts of chaos and its control are reviewed. Both are discussed from an experimental as well as a theoretical viewpoint. Examples are then given of the control of chaos in adiverse set of experimental systems. Current and future applications are discussed.

Chaos computing: implementation of fundamental logical gates by chaotic elements

Basic principles of implementing the most fundamental computing functions by chaotic elements are described. They provide a theoretical foundation of computer architecture based on a totally new principle other than silicon chips. The fundamental functions are: the logical AND, OR, NOT, XOR, and NAND operations (gates) and bit-by-bit arithmetic operations. Each of the logical operations is realized by employing a single chaotic element. Computer memory can be constructed by combining logical gates. With these fundamental ingredients in hand, it is conceivable to build a simple, fast, yet cost effective, general-purpose computing device. Chaos computing may also lead to dynamic architecture, where the hardware design itself evolves during the course of computation.. The basic ideas are explained by employing a one-dimensional model, specifically the logistic map.

Implementation of NOR gate by a chaotic Chua's circuit

We report the experimental implementation of the most fundamental NOR gate with a chaotic Chuas circuit by a simple threshold mechanism. This provides a proof-of-principle experiment to demonstrate the universal computing capability of chaotic circuits in continuous time systems.

Nonlinear antenna technology

Nonlinear antennas combine advances in nonlinear dynamics, active antenna design, and analog microelectronics to generate beam steering and beam forming across an array of nonlinear oscillators. Nonlinear antennas exploit two phenomena typically shunned in traditional designs: nonlinear unit cells and interelement coupling. The design stems from nonlinear coupled differential equation analysis that by virtue of the dynamic control is far less complex than the linear counterparts by eliminating the need for phase shifters and beam forming computers. These advantages arise from incorporating nonlinear dynamics rather than limiting the system to linear quasisteady state operation. A theoretical framework describing beam shaping and beam forming by exploiting the phase, amplitude, and coupling dynamics of nonlinear oscillator arrays is presented. Experimental demonstration of nonlinear beam steering is realized using analog microelectronics.

Introduction to Focus Issue: Intrinsic and Designed Computation: Information Processing in Dynamical Systems— Beyond the Digital Hegemony

How dynamical systems store and process information is a fundamental question that touches a remarkably wide set of contemporary issues: from the breakdown of Moores scaling laws--that predicted the inexorable improvement in digital circuitry--to basic philosophical problems of pattern in the natural world. It is a question that also returns one to the earliest days of the foundations of dynamical systems theory, probability theory, mathematical logic, communication theory, and theoretical computer science. We introduce the broad and rather eclectic set of articles in this Focus Issue that highlights a range of current challenges in computing and dynamical systems.

Removal, Suppression, and Control of Chaos by Nonlinear Design

Techniques to remove, suppress, and control the chaotic behavior of nonlinear systems are reviewed. Analysis of a forced damped nonlinear oscillator provides a brief overview of the relevant nonlinear dynamics of dissipative systems. Various techniques for suppression and control of chaos are then outlined, compared and contrasted. A unified mathematical notation facilitates the comparison. The successes of each strategy in numerical simulations and physical experiments are carefully noted. Their strengths and weaknesses are analyzed, and they are evaluated according to whether they employ feedback, are goal-oriented, are model-based, merely remove chaos–or truly exploit it. An elementary derivation of the important OGY control equation is supplied. Critical references provide an entry into the literature. It is argued that nonlinearity can be a real-world advantage, and it is hoped that this review will serve as summary of, and invitation to, the nascent field of nonlinear design.

Realization of reliable and flexible logic gates using noisy nonlinear circuits

It was shown recently [Murali et al., Phys. Rev. Lett. 102, 104101 (2009)] that when one presents two square waves as input to a two-state system, the response of the system can produce a logical output (NOR/OR) with a probability controlled by the interplay between the system noise and the nonlinearity (that characterizes the bistable dynamics). One can switch or “morph” the output into another logic operation (NAND/AND) whose probability displays analogous behavior; the switching is accomplished via a controlled symmetry-breaking dc input. Thus, the interplay of nonlinearity and noise yields flexible and reliable logic behavior, and the natural outcome is, effectively, a logic gate. This “logical stochastic resonance” is demonstrated here via a circuit implementation using a linear resistor, a linear capacitor and four CMOS-transistors with a battery to produce a cubiclike nonlinearity. This circuit is simple, robust, and capable of operating in very high frequency regimes; further, its ease of implemen...

CONTROL OF HUMAN ATRIAL FIBRILLATION

Chaos control has been applied to control atrial fibrillation in humans. Results are presented on the application and evaluation of chaos control for slowing and regularizing local electrical activation of the right atrium of humans during induced atrial fibrillation.