Adaptive synchronization of drive-response fractional-order complex dynamical networks with uncertain parameters

• We investigate the adaptive synchronization in drive-response fractional-order dynamical networks with uncertain parameters.
• The analytic expression of the controller and the adaptive laws of parameters are introduced.
• The controller has more general and simpler expression form.
• Nodes dynamic need not satisfy the very conservative uniformly Lipschitz condition.

This paper investigates the adaptive synchronization in the drive-response fractional-order dynamical networks with uncertain parameters. By means of both the stability theory of fractional-order differential system and the adaptive control technique, a novel adaptive synchronization controller is developed with a more general and simpler analytical expression, which does not contain the parameters of the complex network, and effective adaptive laws of parameters. Furthermore, the very strong and conservative uniformly Lipschitz condition on the node dynamics of complex network is released. To demonstrate the validity of the proposed method, the examples for the synchronization of systems with the chaotic and hyper-chaotic node dynamics are presented.