Set-reset latch logic operation in a bistable system under suprathreshold and subthreshold signals

Emergent noise-aided logic through synchronization

In this article, we present a dynamical scheme to obtain a reconfigurable noise-aided logic gate that yields all six fundamental two-input logic operations, including the xor operation. The setup consists of two coupled bistable subsystems that are each driven by one subthreshold logic input signal, in the presence of a noise floor. The synchronization state of their outputs robustly maps to two-input logic operations of the driving signals, in an optimal window of noise and coupling strengths. Thus the interplay of noise, nonlinearity, and coupling leads to the emergence of logic operations embedded within the collective state of the coupled system. This idea is manifested using both numerical simulations and proof-of-principle circuit experiments. The regions in parameter space that yield reliable logic operations were characterized through a stringent measure of reliability, using both numerical and experimental data.

Realization of all logic gates and memory latch in the SC-CNN cell of the simple nonlinear MLC circuit

We investigate the State-Controlled Cellular Neural Network framework of Murali-Lakshmanan-Chua circuit system subjected to two logical signals. By exploiting the attractors generated by this circuit in different regions of phase space, we show that the nonlinear circuit is capable of producing all the logic gates, namely, or, and, nor, nand, Ex-or, and Ex-nor gates, available in digital systems. Further, the circuit system emulates three-input gates and Set-Reset flip-flop logic as well. Moreover, all these logical elements and flip-flop are found to be tolerant to noise. These phenomena are also experimentally demonstrated. Thus, our investigation to realize all logic gates and memory latch in a nonlinear circuit system paves the way to replace or complement the existing technology with a limited number of hardware.

Effect of time delay in a bistable synthetic gene network

The essence of logical stochastic resonance is the dynamic manipulation of potential wells. The effect of time delay on the depth of potential wells and the width of a bistable region can be inferred by logic operations in the bistable system with time delay. In a time-delayed synthetic gene network, time delay in the synthesis process can increase the depth of the potential wells, while that in the degradation process, it can reduce the depth of the potential wells, which will result in a decrease in the width of the bistable region (the reason for time delay to induce logic operations without external driving force) and the instability of the system (oscillation). These two opposite effects imply stretching and folding, leading to complex dynamical behaviors of the system, including period, chaos, bubble, chaotic bubble, forward and reverse period doubling bifurcation, intermittency, and coexisting attractors.

Vibrational and stochastic resonances in driven nonlinear systems

Nonlinear systems are abundant in nature. Their dynamics have been investigated very extensively, motivated partly by their multidisciplinary applicability, ranging from all branches of physical and mathematical sciences through engineering to the life sciences and medicine. When driven by external forces, nonlinear systems can exhibit a plethora of interesting and important properties-one of the most prominent being that of resonance. In the presence of a second, higher frequency, driving force, whether stochastic or deterministic/periodic, a resonance phenomenon arises that can generally be termed stochastic resonance or vibrational resonance. Operating a system in or out of resonance promises applications in several advanced technologies, such as the creation of novel materials at the nano, micro and macroscales including, but not limited to, materials having photonic band gaps, quantum control of atoms and molecules as well as miniature condensed matter systems. Motivated in part by these potential applications, this 2-part Theme Issue provides a concrete up-to-date overview of vibrational and stochastic resonances in driven nonlinear systems. It assembles state-of-the-art, original contributions on such induced resonances-addressing their analysis, occurrence and applications from either the theoretical, numerical or experimental perspectives, or through combinations of these. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Vibrational resonances in driven oscillators with position-dependent mass

The vibrational resonance (VR) phenomenon has received a great deal of research attention over the two decades since its introduction. The wide range of theoretical and experimental results obtained has, however, been confined to VR in systems with constant mass. We now extend the VR formalism to encompass systems with position-dependent mass (PDM). We consider a generalized classical counterpart of the quantum mechanical nonlinear oscillator with PDM. By developing a theoretical framework for determining the response amplitude of PDM systems, we examine and analyse their VR phenomenona, obtain conditions for the occurrence of resonances, show that the role played by PDM can be both inductive and contributory, and suggest that PDM effects could usefully be explored to maximize the efficiency of devices being operated in VR modes. Our analysis suggests new directions for the investigation of VR in a general class of PDM systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Periodic and aperiodic force-induced logical stochastic resonance in a bistable system

It was demonstrated recently that there are optimal windows of noise intensity or frequency and amplitude of the periodic driving force, which let a bistable system operate reliably as logic gates. These phenomena are called logical stochastic resonance (LSR). Given that the driving force is not always perfect regular, there may be phase disturbance in driving force; therefore, the Wiener process is used here to model phase disturbance of driving force, and then the effects of phase disturbance on reliability and agility of logic gates are explored in detail. Comparing with the periodic force, the aperiodic force with appropriate intensity phase disturbance can drive a bistable system to yield phenomena similar to LSR in a wider reliable region and can reduce mean switching time to obtain a faster response of logic devices to the input signal. On the other hand, depending on the amplitude and average angular frequency, moderate-intensity phase disturbance may also reduce success probability and increase mean switching time and thus lead to the instability and the slower response of logic devices.