This paper is concerned with the modified function projective synchronization of the uncertain complex dynamic networks with both input nonlinearity and multiple time-varying delay couplings. Firstly, the model of the complex dynamic networks with sector nonlinear input, multiple timevarying delay couplings, model uncertainty and external disturbance is constructed. Then, the adaptive controller is formulated based on the Lyapunov stability theory and the matrix inequality theory, by which the network nodes of the driving system and the response system can realize modified function projective synchronization according to the corresponding function scaling factors. Finally, a four-dimensional hyperchaotic system is considered as the nodes of the complex dynamic networks to achieve numerical simulation. The corresponding theoretical proof and computer simulation are worked out to demonstrate the effectiveness and feasibility of the proposed scheme. INDEX TERMS Complex dynamic networks, multiple time-varying delay couplings, input nonlinearity, modified function projection synchronization, adaptive control.

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This paper deals with the function projective synchronization of two complex dynamic networks with unknown sector nonlinear input, multiple time-varying delay couplings, model uncertainty, and external interferences. Based on Lyapunov stability theory and inequality transformation method, the robust adaptive synchronization controller is designed, by which the drive and response systems can achieve synchronization according to the function scaling factor. Different from some existing studies on nonlinear system with sector nonlinear input, this paper studies the synchronization of two complex dynamic networks when the boundary of sector nonlinear input is unknown. The controller does not include the boundary value of the sector nonlinear input and the time delay term, so it is more practical and relatively easy to implement. The corresponding simulation examples demonstrate the effectiveness of the proposed scheme.

This paper investigates the impulsive synchronization of time delay coupled neural networks. Based on the Lyapunov stability theory and impulsive control method, a distributed delayed impulsive controller is designed to realize synchronization of the coupled neural networks. A new impulsive delayed inequality is proposed, where the control effect of distributed delayed impulses is fully considered. In addition, a suitable Lyapunov-like function is established to prove the stability of the synchronization system. Numerical simulation examples are introduced to illustrate the effectiveness and feasibility of the main results.