Chaos in the fractional order unified system and its synchronization

The chaotic behaviors in the fractional order unified system are numerically investigated. By utilizing the fractional calculus techniques, we found that chaos exists in the fractional order unified system with order less than 3. The lowest order we found to have chaos in this system is 2.76. Chaos synchronization of the fractional order unified system is theoretically and numerically studied using the one-way coupling method. The suitable conditions for achieving synchronization of the fractional order differential system are derived by using the Laplace transform theory. It is noticed that the time required for achieving synchronization of the drive system and the response system and the synchronization effect sensitively depend on the coupling strength. Numerical simulations are performed to verify the theoretical analysis.