2 research outputs found
Stochastic resonance and bifurcation of order parameter in a coupled system of underdamped Duffing oscillators
The long-term mean-field dynamics of coupled underdamped Duffing oscillators
driven by an external periodic signal with Gaussian noise is investigated. A
Boltzmann-type H-theorem is proved for the associated nonlinear Fokker-Planck
equation to ensure that the system can always be relaxed to one of the
stationary states as time is long enough. Based on a general framework of the
linear response theory, the linear dynamical susceptibility of the system order
parameter is explicitly deduced. With the spectral amplification factor as a
quantifying index, calculation by the method of moments discloses that both
mono-peak and double-peak resonance might appear, and that noise can greatly
signify the peak of the resonance curve of the coupled underdamped system as
compared with a single-element bistable system. Then, with the input signals
taken from laboratory experiments, further observations show that the
mean-field coupled stochastic resonance system can amplify the periodic input
signal. Also, it reveals that for some driving frequencies, the optimal
stochastic resonance parameter and the critical bifurcation parameter have a
close relationship. Moreover, it is found that the damping coefficient can also
give rise to nontrivial non-monotonic behaviors of the resonance curve, and the
resultant resonant peak attains its maximal height if the noise intensity or
the coupling strength takes the critical value. The new findings reveal the
role of the order parameter in a coupled system of chaotic oscillators
CHARACTERISTICS OF STOCHASTIC RESONANCE IN ASYMMETRIC DUFFING OSCILLATOR
We study the characteristics of stochastic resonance (SR) in the Duffing oscillator with three types of asymmetries in its double-well potential. The asymmetries controlled by a parameter α are introduced in the potential by varying (i) the depth of the left-well alone, (ii) the location of the minimum of the left-well alone and (iii) both depth and location of the minimum of the left-well alone. The characteristics of SR in the asymmetric cases are different from the symmetric case (α = 1). We find that asymmetry has a strong influence on the optimum noise intensity at which signal-to-noise ratio (SNR) is maximum, mean residence time at resonance and the probability distribution of residence time in the left- and right-wells. For a range of values of α, α = 1, SNR is found to be relatively higher than for α =1