Intrinsic periodic and aperiodic stochastic resonance in an electrochemical cell

In this paper we show the interaction of a composite of a periodic or aperiodic signal and intrinsic electrochemical noise with the nonlinear dynamics of an electrochemical cell configured to study the corrosion of iron in an acidic media. The anodic voltage setpoint $\left(V_0\right)$ in the cell is chosen such that the anodic current $\left(I\right)$ exhibits excitable fixed point behavior in the absence of noise. The subthreshold periodic (aperiodic) signal consists of a train of rectangular pulses with a fixed amplitude and width, separated by regular (irregular) time intervals. The irregular time intervals chosen are of deterministic and stochastic origins. The amplitude of the intrinsic internal noise, regulated by the concentration of chloride ions, is then monotonically increased, and the provoked dynamics are analyzed. The signal to noise ratio and the cross-correlation coefficient versus the chloride ions' concentration curves have a unimodal shape indicating the emergence of an intrinsic periodic or aperiodic stochastic resonance. The abscissa for the maxima of these unimodal curves correspond to the optimum value of intrinsic noise where maximum regularity of the invoked dynamics is observed. In the particular case of the intrinsic periodic stochastic resonance, the scanning electron microscope images for the electrode metal surfaces are shown for certain values of chloride ions' concentrations. These images, qualitatively, corroborate the emergence of order as a result of the interaction between the nonlinear dynamics and the composite signal.

Figure 1

Intrinsic noise-induced system response in the anodic current $I$ for (a) low, (b) medium, and (c) high levels of internal noise superimposed to a subthreshold periodic signal. The setpoint for the autonomous system is $V_0=650\mathrm{mV}$, and the threshold value is $V_{\mathrm{hc}}=500\mathrm{mV}$. The perturbation amplitude is $A=-100\mathrm{mV}$, the time period between pulses is 20 s, and the pulse duration is 2 s. The corresponding chloride ions' concentrations are 0.0125, 0.0249, and 0.0373 M, respectively. (d) The experimentally generated SNR curves as a function of noise level (chloride ions' concentration) for the subthreshold periodic signal perturbation (continuous line) and in the absence of a subthreshold signal [$S\left(t\right)=0$, dashed line]. The indicated points (a)–(c) located on the continuous line correspond to the anodic current time series shown in the left panels. These curves have unimodal shapes confirming the emergence of intrinsic periodic stochastic resonance (IPSR) and ICR, respectively.

Figure 2

SEM images, revealing the morphology of the anode surface at the conclusion of three experimental runs. The images from left to right correspond to the data-points (a)–(c) of the experimentally constructed SNR curve (continuous line) shown in Fig. 1. The corresponding time series are shown in the left panels of Fig. 1.

Figure 3

Intrinsic noise-induced system response in the anodic current $I$ for (a) low, (b) medium, and (c) high levels of internal noise superimposed to a subthreshold aperiodic signal with stochastic ISIs. The setpoint for the autonomous system is $V_0=610\mathrm{mV}$, and the threshold value is $V_{\mathrm{hc}}=320\mathrm{mV}$. The perturbation amplitude is $A=-200\mathrm{mV}$, and the pulse duration is 1 s. The corresponding chloride ions' concentrations are 0.015, 0.035, and 0.05 M, respectively. Notice that the representative portions of the time series, which are shown for each concentration, are of different times in the same subthreshold pulse. This is performed to show the best portion of the recorded time series. (d) The experimentally generated CCC as a function of noise level (chloride ions' concentration) for the subthreshold aperiodic signal perturbation. The indicated points (a)–(c) correspond to the anodic current time series shown in the left panels. This curve has a unimodal shape confirming the emergence of an intrinsic aperiodic stochastic resonance in the noise provoked dynamics.

Figure 4

Intrinsic noise-induced system response in the anodic current $I$ for (a) low, (b) medium, and (c) high levels of internal noise superimposed to a subthreshold aperiodic signal with chaotic ISIs. The setpoint for the autonomous system is $V_0=610\mathrm{mV}$, and the threshold value is $V_{\mathrm{hc}}=320\mathrm{mV}$. The perturbation amplitude is $A=-200\mathrm{mV}$, and the pulse duration is 1 s. The corresponding chloride ions' concentrations are 0.015, 0.035, and 0.055 M, respectively. (d) The experimentally generated CCC as a function of noise level (chloride ions' concentration) for the subthreshold aperiodic signal perturbation. The indicated points (a)–(c) correspond to the anodic current time series shown in the left panels. This curve has a unimodal shape confirming the emergence of an intrinsic aperiodic stochastic resonance in the noise provoked dynamics.