"Rumors on Complex Attractors"
Social psychologists have developed the theory of psychology of rumor, where the traditional focus has been given at the individual level. On the other hand there are studies concerning the dynamics of rumor propagation at a collective level. These studies include experimental data collection as well as mathematical modeling (epidemic models). We consider rumor "invasion" into populations with strong fluctuations in density. Prior to the rumor arrival, the dynamics of the target population is assumed to be at a demographic "steady-state". In fact, it is modeled by a preselected attractor. We assume that while the rumor circulates it divides the target population into two classes; spreaders, and non-spreaders. The transitions between classes are functions of the contact rates and the proportion of spreaders. Will the spreader population survive? and if it does; Will it settle on a different attractor?; How does the dynamics of the rumor compare to the dynamics of its analogue epidemic process? Rumor dispersal between two patches is briefly addressed.