Stochastic resonance via parametric adaptation: Experiments and numerics

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Stochastic resonance via parametric adaptation: Experiments and numerics

Ishant Tiwari, J. M. Cruz, P. Parmananda, and M. Rivera

Phys. Rev. E 100, 060202(R) – Published 6 December 2019

Abstract

In contrast with the conventionally observed mechanism of stochastic resonance (SR) wherein the level of additive noise is systematically varied with a fixed set-point parameter, in this work we report the emergence of the SR phenomena in an electrochemical system maintaining the same level of noise and varying the parametric distance from a homoclinic bifurcation inherent to the system. The experimental system involves the corrosion of a metal disk in an acidic medium under potentiostatic conditions. The applied potential is used as a control parameter and the anodic current generated during the electrodissolution of the metal is the accessible system variable. In the presence of noise, it was observed that the system was able to enhance its output's fidelity with a weak subthreshold input signal when the set point was kept at an optimal parametric distance from the bifurcation. Numerical simulations were performed on a model for this system to corroborate the experimental observations. This type of SR may be critical in scenarios where a biological entity has control only on its sensory parameters and not on the environmental noise amplitude.

Received 23 August 2019

DOI:https://doi.org/10.1103/PhysRevE.100.060202

Physics Subject Headings (PhySH)

Noise

Stochastic dynamical systems

Nonlinear DynamicsInterdisciplinary Physics

Authors & Affiliations

Ishant Tiwari, J. M. Cruz^*, and P. Parmananda

Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai–400 076, India

M. Rivera

Centro de Investigación en Ciencias-(IICBA), UAEM, Avenida Universidad 1001, 62209 Cuernavaca, Morelos, Mexico

^*Present address: Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas, Tuxtla Gutiérrez, Chiapas 29050, Mexico.

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Vol. 100, Iss. 6 — December 2019

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Images

Figure 1
A schematic of the experimental setup used to study the electrodissolution of an iron disk anode (working electrode) in an acidic media (electrolyte). Copper sheet and saturated calomel electrode are the cathode (counterelectrode) and the reference electrode, respectively. The applied potential is controlled with a potentiostat and a USB DAC control card (not shown).
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Figure 2
Time series of the periodic input subthreshold signal (top left panel). System response (anodic current) to the input signal at low (a), optimal (b), and high (c) values of the set point $V_{0}$ . The system response fidelity to the input signal is the best at the optimal set-point value. Cross-correlation coefficient ( $| C_{o} |$ ) between the input and the output is plotted as a function of the set point $V_{0}$ in the right panel (dotted line). The curve shows a unimodal variation as a function of the set point with a maximum at $V_{0} = 450 mV$ , a characteristic observation of stochastic resonance. The marked points (a)–(c) on this curve correspond to the anodic current time series shown in the lower three panels on the left. The amplitude of noise was kept fixed at $D = 185 mV$ while the input pulse amplitude was $- 100 mV$ . The time period between the pulses was 17 s with a pulse duration of 2 s.
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Figure 3
Time series of the aperiodic input subthreshold signal (top left panel). System response (anodic current) to the input signal at low (a), optimal (b), and high (c) values of the set point $V_{0}$ . The system response correlation to the input signal is the best at the optimal set-point value. Cross-correlation coefficient ( $| C_{o} |$ ) between the input and the output is plotted as a function of the set point $V_{0}$ in the right panel (dotted line). The curve shows a unimodal variation as a function of the set point with a maximum at $V_{0} = 470 mV$ , indicating the occurrence of stochastic resonance. The marked points (a)–(c) on this curve correspond to the anodic current time series shown in the lower three panels on the left. The amplitude of noise was kept fixed at $D = 185 mV$ while the input pulse amplitude was $- 100 mV$ . The time period between the pulses was uniformly distributed between 5 and 25 s with a pulse duration of 2 s.
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Figure 4
Numerical simulations: Time series of the periodic input subthreshold signal (top left panel). System response ( $I$ ) to the input signal at low (a), optimal (b), and high (c) values of the set point $v_{0}$ . The system response correlation with the input signal is the best at the optimal set-point value. Normalized cross-correlation coefficient ( $| C_{o} |$ ) between the input and the output is plotted as a function of the set point $v_{0}$ in the right panel (dotted line). The curve shows a unimodal variation as a function of the set point with a maximum at $v_{0} = 29.36$ , indicating the occurrence of stochastic resonance. Cross-correlation coefficient is normalized by the value of $| C_{o} |$ obtained for a superthreshold input signal and zero noise in the system. The $| C_{o} |$ curve (right panel) is an average curve after ten repetitions. The marked points (a)–(c) on the normalized $| C_{o} |$ curve correspond to the current time series $I$ shown in the lower three panels on the left. The amplitude of noise was kept fixed at $D = 1.6$ while the input pulse amplitude was $- 0.133$ . The time period (dimensionless units) between the pulses was 70 with a pulse duration of 15.
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Figure 5
Numerical simulations: Time series of the aperiodic input subthreshold signal (top left panel). System response ( $I$ ) to the input signal at low (a), optimal (b), and high (c) values of the set point $v_{0}$ . The system response correlation with the input signal is the best at the optimal set-point value. Normalized cross-correlation coefficient ( $| C_{o} |$ ) between the input and the output is plotted as a function of the set point $v_{0}$ in the right panel (dotted line). The curve shows a unimodal variation as a function of the set point with a maximum at $v_{0} = 29.37$ , indicating the occurrence of stochastic resonance. Cross-correlation coefficient is normalized by the value of $| C_{o} |$ obtained for a superthreshold input signal and zero noise in the system. The $| C_{o} |$ curve (right panel) is an average curve after ten repetitions. The marked points (a)–(c) on the normalized $| C_{o} |$ curve correspond to the current time series $I$ shown in the lower three panels on the left. The amplitude of noise was kept fixed at $D = 1.6$ while the input pulse amplitude was $- 0.133$ . The time period (dimensionless units) between the pulses was uniformly randomly distributed between 20 and 120 with a pulse duration of 15.
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