Electrochemical Dissolution in the Presence of Time Delayed Feedback

It is well known that time-delayed systems can exhibit rich dynamical behavior ranging from simple oscillations to high-dimensional chaos.[1, 2] Such systems are studied extensively in optoelectronic[3] and biological[4] systems. In electrochemical systems, time-delayed feedback can be used for the control of dynamics, e.g., for the stabilization of unstable steady states and periodic orbits[5]. In this study, the dynamical features of a prototype, negative differential resistance electrochemical model [6] is studied in the presence of various forms of delayed feedback. Specifically, the double layer potential drop is fed back with delay that is either discrete or in a distributed form using a delay kernel. In the latter case, the system was analyzed in a framework of an extended system of ordinary differential equations using an auxiliary variable. The behavior of the system at different parameter values is explored with a virtual space-time representation [7] technique. The features of various virtual spatial states in the form of rotating waves, cluster formation, and turbulence are discussed. Finally, comments are made on possibility of formation of virtual chimera states[8] in the electrochemical system with external delayed feedback.

References:

[1] Giacomelli, G., Marino, F., Zaks, M. A., Yanchuk, S., EPL, Vol. 99, 58005, 2012.

[2] Larger, L., Goedgebuer, J. P., Phys. Rev. E, 69, 036210, 2004.

[3] Larger, L., Proc. R. Soc. A, Vol. 371, 20120464, 2013.

[4] Bocharov, G., Rihan, F. A., J. Comp. and Appl. Math., Vol. 125, 183, 2000.

[5] Kiss, I.Z., Kazsu, Z., and Gaspard, V., Chaos, Vol. 16, 033109, 2006.

[6] Koper, M. T., M., Gaspard, P., J. Chem. Phys., 96, 7797, 1992.

[7] Arrecchi, F. T., Giacomelli, G., Lapucci, A., Meucci, R., Phys. Rev. A., Vol. 45, R4225, 1992.

[8] Larger, L., Penkovsky, B., Maistrenko, Y., Phys. Rev. Lett., Vol. 111, 054103, 2013.