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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.
Highlights
Complex network is a large-scale network with complex topological structure and dynamic behavior, which exists widely in nature and society
Chaotic system is a special kind of nonlinear system, which has the characteristics of initial value sensitivity, unpredictability, strong attractor and so on, so it is often used as the node of complex network in the research of complex network [5]–[6]
Motivated by the above discussion, an adaptive modified function projective synchronization strategy for a class of uncertain complex dynamic networks with sector nonlinear input and multiple time-varying delay couplings is studied in this paper
Summary
Complex network is a large-scale network with complex topological structure and dynamic behavior, which exists widely in nature and society. Reference [34] realized the modified function projective synchronization of complex dynamical network with multiple time-delay couplings and external disturbances. Reference [35] investigated modified function projective synchronization for complex dynamical networks with mixed time-varying and hybrid asymmetric coupling delays. Reference [52] analyzed the synchronization control for a class of master-slave chaotic systems with parameter uncertainties, external noise disturbances and sector nonlinear input. Motivated by the above discussion, an adaptive modified function projective synchronization strategy for a class of uncertain complex dynamic networks with sector nonlinear input and multiple time-varying delay couplings is studied in this paper. We first proposed a new complex dynamic network model which has sector nonlinear input, multiple time-varying delay couplings, model uncertainty and external disturbance. Rn represents an n dimensional Euclidean space; Rn×h represents an n × h real matrix; AT is the transpose of the matrix A; · denotes the Euclidean norm of a vector; I represents the unit matrix; diag {...} represents a block-diagonal matrix; ⊗ represents the Kronecker product; λmax (Q) is the maximum eigenvalue of Matrix Q
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