Generalized dislocated lag function projective synchronization of fractional order chaotic systems with fully uncertain parameters

In this paper, we propose a new method to improve the safety of secure communication. This method uses the generalized dislocated lag projective synchronization and function projective synchronization to form a new generalized dislocated lag function projective synchronization. Moreover, this paper takes the examples of fractional order Chen system and Lü system with uncertain parameters as illustration. As the parameters of the two systems are uncertain, the nonlinear controller and parameter update algorithms are designed based on the fractional stability theory and adaptive control method. Moreover, this synchronization form and method of control are applied to secure communication via chaotic masking modulation. Many information signals can be recovered and validated. Finally, simulations are used to show the validity and feasibility of the proposed scheme.