Asymptotic Hybrid Projection Lag Synchronization of Nonidentical Variable-Order Fractional Complex Dynamic Networks

Significant progress has been made in incorporating fractional calculus into the projection and lag synchronization of complex networks. However, real-world networks are highly complex, making the fractional derivative used in complex dynamics more susceptible to changes over time. Therefore, it is essential to incorporate variable-order fractional calculus into the asymptotic hybrid projection lag synchronization of complex networks. Firstly, this approach considers nonidentical models with variable-order fractional characteristics, which is more general. Secondly, a class of variable-order fractional sliding mode surfaces is designed, and an accurate formula for calculating finite arriving time is provided, in contrast to traditional sliding mode control methods that use an inequality-based range. Thirdly, sufficient conditions for achieving asymptotic hybrid projection lag synchronization of nonidentical variable-order fractional complex networks are derived. Lastly, the feasibility and effectiveness of our approach are demonstrated through two illustrative examples.

Automated summary

Significant progress has been made in incorporating fractional calculus into the projection and lag synchronization of complex networks. However, real-world networks are highly complex, making the fractional derivative used in complex dynamics more susceptible to changes over time. Therefore, it is essential to incorporate variable-order fractional calculus into the asymptotic hybrid projection lag synchronization of complex networks. Firstly, this approach considers nonidentical models with variable-order fractional characteristics, which is more general. Secondly, a class of variable-order fractional sliding mode surfaces is designed, and an accurate formula for calculating finite arriving time is provided, in contrast to traditional sliding mode control methods that use an inequality-based range. Thirdly, sufficient conditions for achieving asymptotic hybrid projection lag synchronization of nonidentical variable-order fractional complex networks are derived. Lastly, the feasibility and effectiveness of our approach are demonstrated through two illustrative examples.