Charge bifurcation structure of a basic RC driven relaxation oscillator

A very simple model of an RC-driven relaxation oscillator is considered. This model retains all the significant properties experimentally observed by many authors in actual circuits, but has the advantage of making it possible to obtain simple and meaningful results. The status of first-order and multiple locking is defined and properties of the sets of values of the bifurcation parameter giving rise to locking or to chaos are investigated. The uniqueness of the value of the parameter that gives rise to locking for fixed values of time lag and rotational number is proved. It is shown how this result can be extended to very general kinds of RC-driven oscillators.<>