Canard Explosion and Coherent Biresonance in the Rate Oscillation of CO Oxidation on Platinum Surface

Abstract

The relationship between canard explosion and coherent biresonance is analyzed by numerically investigating a temporal dynamical model of CO oxidation on Pt surface. Canard explosion, manifesting itself by a dramatic change in the amplitude and period of a periodic orbit within a very narrow interval of a control parameter, is the result of multiple time scales in a dynamical system and is common in excitable systems. Coherent biresonance, namely, two peaks on the signal-to-noise ratio (SNR) curve when varying noise intensity, is a novel phenomenon of coherent resonance which is well-known in excitable systems. When the control parameter is varied from a stable fixed point, crossing the supercritical Hopf bifurcation, one of the peaks that corresponds to relatively larger noise intensity, keeps a constant height and position, while the other becomes higher and moves to lower noise level. When we consider the case in which two control parameters are perturbed by independent noise simultaneously, an interesting picture of one valley between two ridges appears on the 3D surface of SNR.

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

“…The SBR is closely related to the so-called "Canard" bifurcation existing in the deterministic system (1)-(4) [20,22] . As a certain control parameter increases beyond the Hopf bifurcation point, the amplitude and period of the limit cycle first increases slowly, with these small amplitude oscillations being termed as canard trajectory; then, in an exponentially small neighborhood of some critical point, the so-called canard point, the limit cycle explodes, becoming a relaxation oscillator with much larger amplitude and period.…”

“…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] .…”

“…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] .In theoretical studies, however, people have always neglected thermal effect in the systems, and regarded them as isothermal systems. This is much different from the realistic reaction systems.…”

Mixed-mode oscillations in a stochastic, piecewise-linear system

“…Noise-induced MMOs have been described for three coupled FHN systems near a canard [29]. A signal-to-noise ratio may be defined to quantitatively determine dominant frequencies [30]. Noise-induced MMOs may arise via a different mechanism in the case that the Hopf bifurcation is subcritical [31].…”

Can intrinsic noise induce various resonant peaks?

“…An intriguing issue raised is whether a given system may filter with gain in different noise regimes, which would have technological application. After the first proposal of stochastic multiresonance (SMR) [5], the existence of two or more resonant peaks has been predicted for single-mode lasers [6], surface phenomena [7], biological diversity [8] and intracellular calcium oscillations in hepatocytes [9,10], and it has also been described in somewhat more abstract settings [11,12,13,14,15,16]. Though there is no definite claim for experimental evidence of SMR yet, two recent sets of experimental data [17,18] admit such interpretation.…”