Controlling neuronal spikes

We propose two control strategies for achieving desired firing patterns in a physiologically realistic model neuron. The techniques are powerful, efficient, and robust, and we have applied them successfully to obtain a range of targeted spiking behaviors. The methods complement each other: one involves the manipulation of only a parameter, the applied soma current, and the other involves the manipulation of only a state variable, the membrane potential. Both techniques have the advantage that they are not measurement-intensive nor do they involve much run-time computation, as knowledge of only the interspike interval is necessary to implement control

Dynamics based computation

We demonstrate the ability of lattices of coupled chaotic maps to perform simple computations. This dynamical system is shown to emulate logic gates, encode numbers, and perform specific arithmetic operations on those numbers such as addition and multiplication. We also demonstrate the ability of this dynamical system to perform the more specialized operation of determining the least common multiplier of a sequence of integers

Computing with distributed chaos

We describe and discuss in detail some recent results by Sinha and Ditto [Phys. Rev. Lett. 81, 2156 (1998)] demonstrating the capacity of a lattice of threshold coupled chaotic maps to perform computations. Such systems are shown to emulate logic gates, encode numbers, and perform specific arithmetic operations, such as addition and multiplication, as well as yield more specialized operations such as the calculation of the least common multiplier of a sequence of numbers. Furthermore, we extend the scheme to multidimensional continuous time dynamics, in particular to a system relevant to chaotic lasers

Coupling Reduces Noise

We demonstrate how coupling nonlinear dynamical systems can reduce the effects of noise. For simplicity we investigate noisy coupled map lattices. Noise from different lattice nodes can diffuse across the lattice and lower the noise level of individual nodes. We develop a theoretical model that explains this observed noise evolution and show how the coupled dynamics can naturally function as an averaging filter. Our numerical simulations are in excellent agreement with the model predictions

Flexible parallel implementation of logic gates using chaotic elements

We demonstrate the basic principles for the direct and flexible implementation of all basic logical operations utilizing low dimensional chaos. Then we generalize the concept to high dimensional chaotic systems, and show the parallelism inherent in such systems. As a case study we implement the proposed parallel computing architecture to obtain parallelized bit-by-bit addition with a two-dimensional chaotic neuronal and a three-dimensional chaotic laser model

Parallel computing with extended dynamical systems

We discuss the scope of parallelism based on extended dynamical systems, in particular, arrays of chaotic elements. As a case study we demonstrate the rapid solution of the Deutsch-Jozsa problem, utilizing the collective properties of such systems

Realization of the fundamental NOR gate using a chaotic circuit

We report the experimental verification of a simple threshold controller, which clips the chaos to periods of widely ranging orders, in a chaotic circuit. Then we use this to implement the fundamental NOR gate thus obtaining a proof of principle experiment demonstrating the universal computing capability of chaotic systems

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 Moore's 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

Strange nonchaotic stars

The unprecedented light curves of the Kepler space telescope document how the brightness of some stars pulsates at primary and secondary frequencies whose ratios are near the golden mean, the most irrational number. A nonlinear dynamical system driven by an irrational ratio of frequencies generically exhibits a strange but nonchaotic attractor. For Kepler's "golden" stars, we present evidence of the first observation of strange nonchaotic dynamics in nature outside the laboratory. This discovery could aid the classification and detailed modeling of variable stars.Comment: 5 pages, 4 figures, published in Physical Review Letter