title: Delayed feedback induced multirhythmicity in the oscillatory electrodissolution of copper.
abstract: Occurrence of bi- and trirhythmicities (coexistence of two or three stable limit cycles, respectively, with distinctly different periods) has been studied experimentally by applying delayed feedback control to the copper-phosphoric acid electrochemical system oscillating close to a Hopf bifurcation point under potentiostatic condition. The oscillating electrode potential is delayed by τ and the difference between the present and delayed values is fed back to the circuit potential with a feedback gain K. The experiments were performed by determining the period of current oscillations T as a function of (both increasing and decreasing) τ at several fixed values of K. With small delay times, the period exhibits a sinusoidal type dependence on τ. However, with relatively large delays (typically τ ≫ T) for each feedback gain K, there exists a critical delay τcrit above which birhythmicity emerges. The experiments show that for weak feedback, Kτcrit is approximately constant. At very large delays, the dynamics becomes even more complex, and trirhythmicity could be observed. Results of numerical simulations based on a general kinetic model for metal electrodissolution were consistent with the experimental observations. The experimental and numerical results are also interpreted by using a phase model; the model parameters can be obtained from experimental data measured at small delay times. Analytical solutions to the phase model quantitatively predict the parameter regions for the appearance of birhythmicity in the experiments, and explain the almost constant value of Kτcrit for weak feedback.
authors.affiliation: Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA.
authors.forename: Timea
authors.initials: T
authors.lastname: Nagy
authors.affiliation: Department of Physical Chemistry, University of Debrecen, Egyetem tér 1, 4032 Debrecen, Hungary.
authors.forename: Erika
authors.initials: E
authors.lastname: Verner
authors.affiliation: Department of Physical Chemistry, University of Debrecen, Egyetem tér 1, 4032 Debrecen, Hungary.
authors.forename: Vilmos
authors.initials: V
authors.lastname: Gáspár
authors.affiliation: Department of Information Sciences, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan.
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Kori
authors.affiliation: Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA.
authors.forename: István Z
authors.initials: IZ
authors.lastname: Kiss