Adaptive cluster general projective synchronization of complex dynamic networks in finite time

• We give the novel definition of cluster general projective synchronization (CGPS).
• Specially, instead of using impulsive control, intermittent control or hybrid control to reduce the synchronization time, an effective method—finite time synchronization control technique, is applied to achieve cluster synchronization. While little of form paper has been done on this work, which can apply to many practical areas.
• We extend a general network to complex network to achieve adaptive cluster general projective synchronization (CGPS).
• Based on the finite time synchronization control techniques and Lyapunov stability theorem, sufficient conditions are derived to guarantee the realization of adaptive cluster general projective synchronization.
• Numerical simulations will verify the correctness of article's theorem.

This paper investigates adaptive cluster general projective synchronization (CGPS) of complex dynamic networks in finite time. Based on the finite time synchronization control techniques and Lyapunov stability theorem, sufficient conditions are derived to guarantee the realization of adaptive cluster general projective synchronization. Finally, numerical simulation is provided to support the theoretical results.