Construction of Arnold Tongue Structures for Coupled Periodic Oscillators

Arnold tongue structures generated due to the mutual entrainment of two periodic oscillators are studied experimentally and numerically. This mutual entrainment is provoked due to the  mutual (bidirectional) coupling between the two oscillators. In experiments, this bidirectional coupling is achieved by immersing a couple of anodes (oscillators) in a common electrolytic solution. A voltage  mismatch  between these anodes renders the time period of the uncoupled electrochemical oscillators non-identical. Moreover, the coupling strength between the two oscillators is uniquely determined by the distance separating them. Systematically varying the distance between these two anodes as a function of their voltage mismatch, phase locked domains were located. Subsequently, Arnold tongue structures were constructed in the experiments. Numerical simulations, using a model for electrochemical corrosion, corroborate our experimental findings.