Adaptive Modified Function Projective Synchronization for Uncertain Complex Dynamic Networks With Multiple Time-Varying Delay Couplings Under Input Nonlinearity

Abstract

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 time-varying 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.

Keywords

• Complex dynamic networks
• multiple time-varying delay couplings
• input nonlinearity
• modified function projection synchronization
• adaptive control