Synchronization of thermostatically controlled first-order systems

We analyze the collective dynamics of a number of individually heated rooms arranged in the form of a ring. The temperature of each room is kept within a given band by a thermostat which makes it behave as a self-sustained oscillator. Each room interacts thermally only with its immediate neighbors and with the exterior. The temperature in each room is modeled by a first-order differential equation. Numerical results of the complete system show the presence of a rich array of synchronization dynamics in frequency and phase as well as clustering and coupling-induced amplitude death.