Arnold Tongue of Electrochemical Nonlinear Oscillators

We study the Arnold tongue of a nonlinear electrochemical oscillator entrained to an electrical periodic forcing. In our system, the width of the 1:3 entrainment region was broader than that of the 1:2 region. The 1: 1 and 1:3 regions became monotonically broad when the conductance of the electrode cell was increased by the electrochemical redox reaction of Fe(CN)(6)(4-) reversible arrow Fe(CN)(6)(3-) + e. In contrast, the 1:2 region changed nonmonotonically. In particular, the rate of change in the 1:2 region was greater than those of the 1: 1 and 1:3 regions. These experimental results were qualitatively reproduced by the use of phase response curves of a corresponding mathematical model. We also discuss higher harmonics included in a limit cycle describing the isolated oscillator, dependence on the redox reaction, and hysteresis due to a bistability.