| From an ecological and evolutionary biology perspective, the allocation process of animals to resources may be modeled as an optimization process. The "ideal free distribution" (IFD) results from such a process, and characterizes a particular distribution, where each animal adopts a strategy that results in equal fitness for all. The IFD is optimal in the sense that a unilateral deviation by an animal from this strategy would result in fitness degradation to itself and other animals. This dissertation analyzes the emergence of IFD distributions from two different perspectives.; First, we develop both discrete and continuous generic models, where we view the optimization process as being driven by the motion dynamics of a fixed number of agents across a static graph (i.e., where each node represents an allocation strategy and the graph's topology constrains how agents can switch from one strategy to another). We derive general sensing and motion conditions on the agents that guarantee that an IFD will emerge. Our interest is motivated by several applications in cooperative control, in particular, in cooperative surveillance missions, where IFD-based strategies are useful in solving the problem of dynamic allocation of vehicles.; Second, we ignore the agents' dynamics, and view the IFD as the result of the evolution of a graph's dynamic topology. We introduce a generic set of dynamical equations which captures the broad tendencies of the connectivity dynamics of a growing graph, and lead to the emergence of IFDs. We derive particular conditions which guarantee that if IFDs result from the evolution of a graph's dynamic topology, then the connectivity distribution of the nodes will become scale-free. |
