Construction of logic gates exploiting resonance phenomena in nonlinear systems

2021 ◽  
Vol 379 (2192) ◽  
pp. 20200238 ◽  
Author(s):  
K. Murali ◽  
S. Rajasekar ◽  
Manaoj V. Aravind ◽  
Vivek Kohar ◽  
W. L. Ditto ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Stochastic Resonance ◽  
Logic Gates ◽  
Bistable System ◽  
Periodic Forcing ◽  
Vibrational Resonance ◽  
Logic Function ◽  
Excitable Systems ◽  
Influence Of Noise ◽  
Optimal Window

A two-state system driven by two inputs has been found to consistently produce a response mirroring a logic function of the two inputs, in an optimal window of moderate noise. This phenomenon is called logical stochastic resonance (LSR). We extend the conventional LSR paradigm to implement higher-level logic architecture or typical digital electronic structures via carefully crafted coupling schemes. Further, we examine the intriguing possibility of obtaining reliable logic outputs from a noise-free bistable system, subject only to periodic forcing, and show that this system also yields a phenomenon analogous to LSR, termed Logical Vibrational Resonance (LVR), in an appropriate window of frequency and amplitude of the periodic forcing. Lastly, this approach is extended to realize morphable logic gates through the Logical Coherence Resonance (LCR) in excitable systems under the influence of noise. The results are verified with suitable circuit experiments, demonstrating the robustness of the LSR, LVR and LCR phenomena. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

Different fast excitations on the improvement of stochastic resonance in bounded noise excited system

2020 ◽  
Vol 34 (26) ◽  
pp. 2050238
Author(s):  
Huayu Liu ◽  
Jianhua Yang ◽  
Houguang Liu ◽  
Shuai Shi
Keyword(s):  
Stochastic Resonance ◽  
Circuit Simulation ◽  
Bistable System ◽  
Key Factors ◽  
Vibrational Resonance ◽  
Bounded Noise ◽  
High Frequency Signal ◽  
Excited System ◽  
Improvement Effect ◽  
Fast Excitation

Stochastic resonance is significant for signal detection. In this paper, a method to improve the stochastic resonance performance in a bistable system excited by bounded noise is studied. Specifically, we add a high-frequency signal to the system as an auxiliary excitation to induce vibrational resonance and focus on the influence of the auxiliary excitation waveform on the improvement effect. We investigate the stochastic resonance performance improved by a fast excitation in different waveforms through numerical simulations. The results show that, the improvement effect of the stochastic resonance depends on the waveform of the fast excitation closely. The symmetry property and constant component of the fast excitation are two key factors. Further, we accomplish the circuit simulation by constructing a circuit to generate bounded noise and the circuit of the bistable system.

scholarly journals Stochastic and vibrational resonance in complex networks of neurons

2021 ◽  
Vol 379 (2198) ◽  
Author(s):  
Ali Calim ◽  
Tugba Palabas ◽  
Muhammet Uzuntarla
Keyword(s):  
Nonlinear Systems ◽  
Complex Networks ◽  
Stochastic Resonance ◽  
Network Architecture ◽  
External Perturbation ◽  
Neural System ◽  
Neural Systems ◽  
Vibrational Resonance ◽  
Resonance Phenomena ◽  
Information Signal

The concept of resonance in nonlinear systems is crucial and traditionally refers to a specific realization of maximum response provoked by a particular external perturbation. Depending on the system and the nature of perturbation, many different resonance types have been identified in various fields of science. A prominent example is in neuroscience where it has been widely accepted that a neural system may exhibit resonances at microscopic, mesoscopic and macroscopic scales and benefit from such resonances in various tasks. In this context, the two well-known forms are stochastic and vibrational resonance phenomena which manifest that detection and propagation of a feeble information signal in neural structures can be enhanced by additional perturbations via these two resonance mechanisms. Given the importance of network architecture in proper functioning of the nervous system, we here present a review of recent studies on stochastic and vibrational resonance phenomena in neuronal media, focusing mainly on their emergence in complex networks of neurons as well as in simple network structures that represent local behaviours of neuron communities. From this perspective, we aim to provide a secure guide by including theoretical and experimental approaches that analyse in detail possible reasons and necessary conditions for the appearance of stochastic resonance and vibrational resonance in neural systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

scholarly journals Vibrational and stochastic resonances in driven nonlinear systems

2021 ◽  
Vol 379 (2192) ◽  
pp. 20200226 ◽  
Author(s):  
U. E. Vincent ◽  
P. V. E. McClintock ◽  
I. A. Khovanov ◽  
S. Rajasekar
Keyword(s):  
Nonlinear Systems ◽  
Stochastic Resonance ◽  
Quantum Control ◽  
Resonance Phenomenon ◽  
Theme Issue ◽  
Vibrational Resonance ◽  
Potential Applications ◽  
Mathematical Sciences ◽  
External Forces ◽  
Photonic Band

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)’.

scholarly journals Vibrational and stochastic resonances in driven nonlinear systems: part 2

2021 ◽  
Vol 379 (2198) ◽  
Author(s):  
U. E. Vincent ◽  
P. V. E. McClintock ◽  
I. A. Khovanov ◽  
S. Rajasekar
Keyword(s):  
Nonlinear Systems ◽  
Stochastic Resonance ◽  
State Of The Art ◽  
Ambient Vibration ◽  
Nonlinear Phenomena ◽  
Engineering Systems ◽  
Stochastic Excitation ◽  
Theme Issue ◽  
Vibrational Resonance ◽  
And Control

Nonlinearity is ubiquitous in both natural and engineering systems. The resultant dynamics has emerged as a multidisciplinary field that has been very extensively investigated, due partly to the potential occurrence of nonlinear phenomena in all branches of sciences, engineering and medicine. Driving nonlinear systems with external excitations can yield a plethora of intriguing and important phenomena—one of the most prominent being that of resonance. In the presence of additional harmonic or stochastic excitation, two exotic forms of resonance can arise: vibrational resonance or stochastic resonance, respectively. Several promising state-of-the-art technologies that were not covered in part 2 of this theme issue are discussed here. They include inter alia the improvement of image quality, the design of machines and devices that exert vibrations on materials, the harvesting of energy from various forms of ambient vibration and control of aerodynamic instabilities. They form an important part of the theme issue as a whole, which is dedicated to an overview of vibrational and stochastic resonances in driven nonlinear systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

scholarly journals Delay-induced resonance suppresses damping-induced unpredictability

2021 ◽  
Vol 379 (2192) ◽  
pp. 20200232 ◽  
Author(s):  
M. Coccolo ◽  
J. Cantisán ◽  
J. M. Seoane ◽  
S. Rajasekar ◽  
M. A. F. Sanjuán
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Stochastic Resonance ◽  
Duffing Oscillator ◽  
Critical Values ◽  
Minimal Amount ◽  
Combined Effects ◽  
Theme Issue ◽  
Vibrational Resonance ◽  
The Right

Combined effects of the damping and forcing in the underdamped time-delayed Duffing oscillator are considered in this paper. We analyse the generation of a certain damping-induced unpredictability due to the gradual suppression of interwell oscillations. We find the minimal amount of the forcing amplitude and the right forcing frequency to revert the effect of the dissipation, so that the interwell oscillations can be restored, for different time delay values. This is achieved by using the delay-induced resonance, in which the time delay replaces one of the two periodic forcings present in the vibrational resonance. A discussion in terms of the time delay of the critical values of the forcing for which the delay-induced resonance can tame the dissipation effect is finally carried out. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

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