Sudeshna Sinha

Adaptive control in nonlinear dynamics

Abstract We extend an adaptive control algorithm recently suggested by Huberman and Lumer to multi-parameter and higher- dimensional nonlinear systems. This control mechanism is remarkably effective in returning a system to its original dynamics after a sudden perturbation in the system parameters changes the dynamical behaviour. We find that in all cases, the recovery time is linearly proportional to the inverse of control stiffness (for small stiffness). In higher dimensions there is an additional optimization problem since increasing stiffness beyond a certain value can retard recovery. The control of fixed point dynamics in systems capable of a wide variety of dynamical behaviour is demonstrated. We further suggest methods by which periodic motion such as limit cycles can be adaptively controlled, and demonstrate the robustness of the procedure in the presence of (additive) background noise.

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.

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.

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...

Evidence of universality for the May-Wigner stability theorem for random networks with local dynamics

We consider a random network of nonlinear maps exhibiting a wide range of local dynamics, with the links having normally distributed interaction strengths. The stability of such a system is examined in terms of the asymptotic fraction of nodes that persist in a nonzero state. Scaling results show that the probability of survival in the steady state agrees remarkably well with the May-Wigner stability criterion derived from linear stability arguments. This suggests universality of the complexity-stability relation for random networks with respect to arbitrary global dynamics of the system.

Synthetic gene networks as potential flexible parallel logic gates

We show how a synthetic gene network can function, in an optimal window of noise, as a robust logic gate. Interestingly, noise enhances the reliability of the logic operation. Further, the noise level can also be used to switch logic functionality, for instance toggle between AND, OR and XOR gates. We also consider a two-dimensional model of a gene network, where we show how two complementary gate operations can be achieved simultaneously. This indicates the flexible parallel processing potential of this biological system.

Order in the turbulent phase of globally coupled maps

Abstract The broad peaks seen in the power spectra of the mean field in a globally coupled map system indicate a subtle coherence between the elements, even in the “turbulent” phase. These peaks are investigated in detail with respect to the number of elements coupled, nonlinearity and global coupling strengths. We find that this roughly periodic behavior also appears in the probability distribution of the mapping, which is therefore not invariant. We also find that these peaks are determined by two distinct components: effective renormalization of the nonlinearity parameter in the local mappings, and the strength of the mean field interaction term. Finally, we demonstrate the influence of background noise on the peaks, which is quite counterintuitive, as they become sharper with increase in strength of the noise, up to a certain critical noise strength.

Chaogates: Morphing logic gates that exploit dynamical patterns

Chaotic systems can yield a wide variety of patterns. Here we use this feature to generate all possible fundamental logic gate functions. This forms the basis of the design of a dynamical computing device, a chaogate, that can be rapidly morphed to become any desired logic gate. Here we review the basic concepts underlying this and present an extension of the formalism to include asymmetric logic functions.

Chaos computing: ideas and implementations.

We review the concept of the ‘chaos computing’ paradigm, which exploits the controlled richness of nonlinear dynamics to obtain flexible reconfigurable hardware. We demonstrate the idea with specific schemes and verify the schemes through proof-of-principle experiments.