Theory of Incursive Synchronization and Application to the Anticipation of a Chaotic Epidemic

This paper deals with a general theory of synchronization of systems coupled by an incursive connection. For systems with a time shift, the slave or driven system anticipates the values of the master or driver system by a future time period giving rise to an anticipatory synchronization. Some extensions show the possibility to enhance the anticipatory synchronization, what we call meta-anticipatory synchronization. An application is shown in the case of an epidemic system represented by a chaotic delayed Pearl-Verhulst map representing the incubation duration of infected susceptibles. A slave model of the infected population is incursively synchronized to the infected population master system, the simulation of which showing that the infected population can be anticipated by a time duration equal to the incubation period.