Effects of noise near a homoclinic bifurcation in an electrochemical system

Abstract

The interaction of external noise with an electrochemical oscillator (anodic dissolution of iron) has been studied experimentally on both sides of the homoclinic bifurcation. In the oscillatory regime the regularity of the limit cycle behavior was destroyed with increasing noise amplitude until no periodicity was observable any more. In contrast, the response of the excitable state (fixed point regime) became more regular at intermediate noise levels.

Experimental observation of strange nonchaotic attractors in a driven excitable system

“…The two main types of dynamics observed were the fixed point behavior (constant current response) and period-1 oscillations emerging from a supercritical Hopf bifurcation at ≈ 180 mV. For increasing voltage, typical relaxation oscillations resulted, whose period incremented as the voltage is increased until eventually they die out in a homoclinic bifurcation at about 240 mV [11]. Although the qualitative features of the experimental bifurcation diagram are robust and therefore preserved from one experimental run to another, the exact values for the different bifurcation points do vary slightly.…”

“…Oscillations in anodic current I (the current between the anode and the cathode) were recorded using a 12-bit data acquisition card at a sampling rate of 250 S/s. Before subjecting the anodic voltage of the electrochemical cell to quasiperiodic forcing, an experimental bifurcation diagram of the autonomous system was constructed [11] using the cyclic voltammogram method. Varying anodic voltage (V ) as the scan parameter, different dynamical responses of the anodic current (I ) were mapped out [11][12][13].…”

“…Before subjecting the anodic voltage of the electrochemical cell to quasiperiodic forcing, an experimental bifurcation diagram of the autonomous system was constructed [11] using the cyclic voltammogram method. Varying anodic voltage (V ) as the scan parameter, different dynamical responses of the anodic current (I ) were mapped out [11][12][13]. The other system parameters like electrolyte concentration and temperature of the cell were maintained constant.…”

Stochastic bi-resonance in non-isothermal carbon monoxide catalytic oxidation system

“…In the last two decades, the constructive role of noise, especially stochastic resonance (SR), has been widely studied [11] . In the last ten years, the SR in chemical systems has gained growing studies [12][13][14][15][16][17][18][19][20] . Intriguingly, people have found SR in electrochemical experiments [12][13][14] .…”

“…In the last ten years, the SR in chemical systems has gained growing studies [12][13][14][15][16][17][18][19][20] . Intriguingly, people have found SR in electrochemical experiments [12][13][14] . In theoretical studies, the SCRS has received much more studies [15][16][17][18][19][20] , in which various SR behaviors have been found, including the external signal SR (ESSR) [15,16] , the internal signal SR (ISSR) [17] , the internal noise SR (INSR) [18,19] , and stochastic bi-resonance (SBR) [20] .…”