Synchronization and anti-synchronization of chaotic systems: A differential and algebraic approach

Chaotic systems synchronization and anti-synchronization problems are tackled by means of differential and algebraic techniques for nonlinear systems. An algebraic observer is proposed for systems satisfying an algebraic observability condition. This observer can be used as a slave system whose states are synchronized with the master (chaotic) system. This approach has the advantages of being independent of the chaotic nature of the master system, it uses a reduced set of measurable signal from the master system and it also solves the anti-synchronization problem as a straightforward extension of the synchronization one. A Colpitts oscillator is given to illustrate the effectiveness of the suggested approach.