TEMPERATURE SYNCHRONIZATION, PHASE DYNAMICS AND OSCILLATION DEATH IN A RING OF THERMALLY-COUPLED ROOMS

Synchronization of coupled, self-excited oscillators in complex systems is a common occurance. This report examines the effects of thermal coupling through the walls of a building on temperature oscillations due to hysteretic thermostatic control. The specific case of three rooms is studied. A system of differential equations models the dynamics of each room temperature, accounting for on-off heating, heat loss to the environment, and heat exchange between rooms. Three types of solutions are observed: one in which all room temperatures oscillate in phase, another with the oscillations equidistant in phase, and a third that is time-independent. The existence and linear stability of each solution type is investigated as a function of a parameter k that represents the thermal interaction between neighboring rooms. The in-phase behavior exists and is linearly stable for all k, the out-of-phase oscillations exist in a band of k and are stable in a smaller band, and the time-independent solution exists above a certain k where they are stable.Copyright © 2011 by ASME

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