  Motivated by the dynamics of micro-scale oscillators with thermo-optical
feedback, a simplified third order model, capturing the key features of these
oscillators is developed, where each oscillator consists of a displacement
variable coupled to a temperature variable. Further, the dynamics of a pair of
such oscillators coupled via a linear spring is analyzed. The analytical
procedures used are the variational equation method and the two-variable
expansion method. It is shown that the analytical results are in agreement with
the results of numerical integration. The bifurcation structure of the system
is revealed through a bifurcation diagram.
