Vibrational and stochastic resonances in driven nonlinear systems

Abstract

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 and stochastic resonances in driven nonlinear systems: part 2

“…The general content of the theme issue has been described explicitly in part 1 [ 18 ] and organized with papers in three broad domains: theory, methods and analysis; complex networks and experimental applications. While a few articles in part 1 presented analysis on position-dependent mass systems [ 21 ], delayed feedback-induced resonances in deformable potential system [ 22 ] and Duffing oscillator [ 23 ], and driven two-level quantum systems [ 24 ], part 2 assembles state-of-the-art, original contributions on VR and SR in some systems not covered by part 1.…”

“…Among the phenomenon associated with multi-frequency driving, vibrational and stochastic resonances form the focus of this theme issue. They are arguably the most prominent forms of nonlinear resonance to have been investigated in the last 20 years, probably on account of the number of potential applications and ease of implementation [ 17 , 18 ].…”

“…The phenomenon of resonance, its definitions and its occurrence in biological, chemical, physical, mechanical and engineering systems were discussed in the introductory article of part 1 of this theme issue [ 18 ]. The concepts of vibrational resonance (VR) and stochastic resonance (SR), their origin, similarities and differences [ 19 ] in the context of driving forces as well as their manifestations and applications [ 3 , 5 , 15 , 20 ] were all described there.…”

Resonance as a Design Strategy for AI and Social Robots

“…For instance, in a review of magnetic resonance, “the term resonance implies that we are in tune with a natural frequency of the magnetic system” (Slichter, 2013 ). Yet a recent Royal Society review article (Vincent et al, 2021 ) makes the following claim: “the definition of resonance has been generalized [to include] all known processes leading to the enhancement, suppression or optimization of a system's response through the variation/perturbation/modulation of any system property.” This incredibly broad definition of resonance in physics suggests the challenge and need for a coherent understanding of this important concept across physics, neuroscience, the social sciences and design.…”

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

“…LVR has been realized in a twopotential system 25,26,61 . Besides logic gates, LSR and LVR can be used to realize SR flip-flops [62][63][64][65] . Then the question arises whether LSR and LVR can produce all the logic gates including XOR gate when one employs a bistable system.…”