The generalized synchronization of fractional order systems is investigated, including the synchronization between two different fractional order systems with the same order, the synchronization between two different fractional order systems with no orders the same, and the synchronization between a classical system and its corresponding fractional order system with mismatched parameters. The mechanism for the occurrence of generalized synchronization of fractional order systems is clarified, the necessary and sufficient conditions are given, and several methods to detect generalized synchronization are discussed. The relationship between generalized synchronization and the equivalence of fractional order systems is also considered.

• Received 15 August 2006

DOI:https://doi.org/10.1103/PhysRevE.75.056201