ABSTRACT
Likewise, if one ormore of the thermostats had a rule where the room temperature was a nonlinear function of past temperature, this would introduce dynamic complexity into the system andmake its future behavior evenmore difficult to predict. For example, if one of our thermostats had the internal ruleTtþ1 ¼ cTt-cTt2,whereTtþ1 is the room temperature for the next time period, Tt is the current temperature setting of the thermostat and c is a constant, then the system would have a very interesting range of behaviors. This simple nonlinear dynamic equation is known as the logisticmap.Depending on the initial temperature and the value of the constant c, the system could do anything from going to a steady state, to regular oscillations, to swinging around chaotically. Such a system is sensitive to both initial conditions and path dependent. The key point is it is difficult or even impossible for an outside observer to predict the future path of a system with such a nonlinear relationship without both knowing the rule, its parameters and the initial conditions.
