Chaos synchronization between two identical restricted three body problem via active control and adaptive control method

Abstract

This article presents the chaos synchronization problem of the restricted three body problem (RTBP) when the massive primary is supposed to be oblate spheroid and the smaller one is a uniform circular ring. The feedback controller for the stability of the closed-loop system are designed using the active control and adaptive control strategy. It is shown that the two methods have excellent performance, with the active control marginally outperforming the adaptive control in terms of transient analysis. Simulation results satisfy the theoretical findings. For validation of results by numerical simulations, the Mathematica 10 is used when the primaries are Saturn and Jupiter.