  The sectoral synchronization observed for the Japanese business cycle in the
Indices of Industrial Production data is an example of synchronization. The
stability of this synchronization under a shock, e.g., fluctuation of supply or
demand, is a matter of interest in physics and economics. We consider an
economic system made up of industry sectors and goods markets in order to
analyze the sectoral synchronization observed for the Japanese business cycle.
A coupled oscillator model that exhibits synchronization is developed based on
the Kuramoto model with inertia by adding goods markets, and analytic solutions
of the stationary state and the coupling strength are obtained. We simulate the
effects on synchronization of a sectoral shock for systems with different price
elasticities and the coupling strengths. Synchronization is reproduced as an
equilibrium solution in a nearest neighbor graph. Analysis of the order
parameters shows that the synchronization is stable for a finite elasticity,
whereas the synchronization is broken and the oscillators behave like a giant
oscillator with a certain frequency additional to the common frequency for zero
elasticity.
