Modeling and analysis for a temperature system based on resource dynamics and the ideal free distribution

Bioinspired design approaches seek to exploit nature in order to construct robust and optimal solutions. One useful concept from behavioral ecology is the ideal free distribution (IFD). Here, we relax the IFD main assumptions using the standing crop idea to introduce dynamics to the resources. Using the IFD, the standing crop, and the replicator dynamics concepts, we make some analogies with a temperature control in order to get a maximum uniform temperature. We analytically show that the equilibrium point of the system (i.e., the IFD) is a locally asymptotically stable point, and it is a globally asymptotically stable point for one special case.