Enhancement and weakening of stochastic resonance for a coupled system

Abstract

In the paper, we investigate the phenomenon of stochastic resonance of a system with finite locally coupled linear elements driven by multiplicative dichotomous noise and temporal periodic signal. It is shown that, for some suitably selected values of the parameters, with increasing the size of the system or the coupling among the nearest elements, the stochastic resonance phenomenon can be enhanced; while for some other suitably selected parameters' values, with the increase of the size or the coupling, the phenomenon of stochastic resonance can be weakened. Our results can provide some useful insights for the investigation of the stochastic resonance phenomenon of the systems with locally (or globally) coupled finite (or infinite) elements.

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

“…The type of resonance depends largely on the matching method as well as on the nature of the external driving force that produces it [11] , [12] . Vibrational resonance, for example, occurs in dual-frequency-driven non-linear systems with distinct frequencies [7] , [8] , [9] , [10] , [13] , [14] , [15] , [16] , [17] , [18] , [19] ; stochastic resonance (SR) occurs when one of the two forces is replaced with noise of appropriate intensity [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] ; and chaotic resonance takes place when the high-frequency component of the driving force is replaced with the output from a chaotic system [29] , [30] , [31] . Other forms of resonance include coherence resonance [32] , [33] , [34] , ghost resonance [21] , [35] , [36] and autoresonance [37] , [38] , parametric resonance [39] , [40] , [41] , as well as conventional resonance in the form of harmonic, subharmonic and ultraharmonic resonances [42] , [43] , [44] .…”

Vibrational resonance in an oscillator with an asymmetrical deformable potential

“…Next, we describe the system's vibrations in terms of the deviation of slow motion χ from the equilibrium points χ * , using the deviation variable Y (= χ − χ * ) in Eq. (18). The equilibrium points around which slow oscillation can occur are χ * min(max) = 2nπ, where n is an integer.…”

“…VR occurs in bi-harmonically driven non-linear systems when there is a large difference between the frequencies of the two driving forces -one of which is a fast oscillation at frequency much higher than that of the slower "signal". In VR, the noise in the stochastic resonance case [2,7,[16][17][18] or chaotic system for chaotic resonance [4][5][6] is replaced by a high-frequency input leading, for appropriately chosen parameters, to an enhancement in the system's response to the slow signal. Such amplification takes place when the response amplitude becomes minimum at the bifurcation of the effective potential.…”

Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency*

“…[4][5][6][7][8][9][10][11][12][13] However, many recent investigations show that SR can also occur in linear systems with multiplicative colored noise. [14][15][16][17][18][19][20][21][22][23][24] As a classical model, harmonic oscillators [25] are widely used to describe various natural phenomena. Thus, the research on harmonic oscillators have draw more and more attention.…”

“…In most previous studies, the impact of environmental fluctuations on each coupled particle is assumed to be identical, [17,19,31] which means the same noise will be added to each coupled oscillator. In realistic situations, although the coupled particles are in the same environment, the fluctuation noises acting on them are only independently and identically distributed, not exactly the same.…”