Mixed-mode oscillations and incomplete homoclinic scenarios to a saddle focus in the indium/thiocyanate electrochemical oscillator

Abstract

The complex mixed-mode and chaotic oscillations in the reduction of indium(III) at a hanging mercury drop electrode in thiocyanate solution are studied in experimental detail in the parameter plane. With the aid of a simple model developed previously, we critically discuss the relation of the experimentally observed periodic–chaotic sequences with those predicted by the Shil’nikov theory of homoclinic orbits. It appears helpful to distinguish between two fundamentally different types of mixed-mode behavior: ‘‘type 1’’ related to the incomplete homoclinic scenarios observed in the present system and its model; ‘‘type 2’’ related more directly to the Shil’nikov behavior and the classical Rössler type of reinjection mechanism. The definitions and properties of both types of mixed-mode oscillation are worked out in some detail.