Theory of Computing Anticipatory Systems Based on Differential Delayed-Advanced Difference Equations

Abstract

This paper introduces some computing anticipatory systems based on differential delayed‐advanced difference equations. Delayed systems are systems which are based on a memory of past states and advanced systems are systems which depend explicitly on their anticipatory future potential states. As any physical actual systems, the laws of evolution must be defined at the current time, so, the past and future states are to be defined by new variables defined at the current time taking into account some hidden mechanisms for their existence and knowledge at the current time, because the past states do no more exist at the current time, and the future states are not yet actualized. Several analytical methods are developed to show properties typical of anticipatory systems. Some delayed‐advanced systems can be transformed to differential equations defined at the current time. Mathematically, new variables, defined by equations at the current time, are introduced in view of computing, by synchronization, past and/or future states. Some other anticipatory systems can be transformed to delayed systems. Numerical simulations of such computing anticipatory systems are presented.