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)’.

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 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)’.

Periodic Flows to Chaos Based on Discrete Implicit Mappings of Continuous Nonlinear Systems

2015 ◽  
Vol 25 (03) ◽  
pp. 1550044 ◽  
Author(s):  
Albert C. J. Luo
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Nonlinear Dynamical Systems ◽  
Duffing Oscillator ◽  
Single Step ◽  
Nonlinear Dynamical ◽  
Periodic Flows ◽  
Mapping Structures ◽  
Stability And Bifurcations

This paper presents a semi-analytical method for periodic flows in continuous nonlinear dynamical systems. For the semi-analytical approach, differential equations of nonlinear dynamical systems are discretized to obtain implicit maps, and a mapping structure based on the implicit maps is employed for a periodic flow. From mapping structures, periodic flows in nonlinear dynamical systems are predicted analytically and the corresponding stability and bifurcations of the periodic flows are determined through the eigenvalue analysis. The periodic flows predicted by the single-step implicit maps are discussed first, and the periodic flows predicted by the multistep implicit maps are also presented. Periodic flows in time-delay nonlinear dynamical systems are discussed by the single-step and multistep implicit maps. The time-delay nodes in discretization of time-delay nonlinear systems were treated by both an interpolation and a direct integration. Based on the discrete nodes of periodic flows in nonlinear dynamical systems with/without time-delay, the discrete Fourier series responses of periodic flows are presented. To demonstrate the methodology, the bifurcation tree of period-1 motion to chaos in a Duffing oscillator is presented as a sampled problem. The method presented in this paper can be applied to nonlinear dynamical systems, which cannot be solved directly by analytical methods.

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)’.

scholarly journals Role of thermal field in entanglement harvesting between two accelerated Unruh-DeWitt detectors

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Dipankar Barman ◽  
Subhajit Barman ◽  
Bibhas Ranjan Majhi
Keyword(s):  
Mutual Information ◽  
Critical Point ◽  
Thermal Field ◽  
Narrow Range ◽  
Critical Value ◽  
Critical Values ◽  
Parallel Motion ◽  
Field Temperature ◽  
The Right

Abstract We investigate the effects of field temperature T(f) on the entanglement harvesting between two uniformly accelerated detectors. For their parallel motion, the thermal nature of fields does not produce any entanglement, and therefore, the outcome is the same as the non-thermal situation. On the contrary, T(f) affects entanglement harvesting when the detectors are in anti-parallel motion, i.e., when detectors A and B are in the right and left Rindler wedges, respectively. While for T(f) = 0 entanglement harvesting is possible for all values of A’s acceleration aA, in the presence of temperature, it is possible only within a narrow range of aA. In (1 + 1) dimensions, the range starts from specific values and extends to infinity, and as we increase T(f), the minimum required value of aA for entanglement harvesting increases. Moreover, above a critical value aA = ac harvesting increases as we increase T(f), which is just opposite to the accelerations below it. There are several critical values in (1 + 3) dimensions when they are in different accelerations. Contrary to the single range in (1 + 1) dimensions, here harvesting is possible within several discrete ranges of aA. Interestingly, for equal accelerations, one has a single critical point, with nature quite similar to (1 + 1) dimensional results. We also discuss the dependence of mutual information among these detectors on aA and T(f).

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