Abstract
This paper studies the modified function projective synchronization of uncertain complex dynamic network model with multiple time-delay couplings and external disturbances. Based on Lyapunov stability theory, the positive definite function is designed and the sufficient conditions of synchronization are given. Both the uncertain parameters and the unknown bounded disturbances are estimated in accordance with the adaptive laws. With the adaptive feedback controller, the complex dynamic network can synchronize with reference node by a scaling function matrix. The reference node can be periodic orbit, equilibrium point, or a chaotic attractor. Finally, two numerical simulations are offered to illustrate the effectiveness of the proposed method.
Highlights
Complex networks widely exist in various fields of science and engineering, ranging from biology, physics, and chemistry to social networks and technological applications
This paper studies the modified function projective synchronization of uncertain complex dynamic network model with multiple time-delay couplings and external disturbances
In [26], Du et al achieved the function projective synchronization for general complex dynamical networks with constant or time-varying time-delay coupling by a hybrid feedback control method, but the model uncertain and external disturbances were not taken into account
Summary
Complex networks widely exist in various fields of science and engineering, ranging from biology, physics, and chemistry to social networks and technological applications. Reference [24] proposed an adaptive controller to investigate the problem of function projective synchronization in complex dynamical networks with constant time-delay coupling, uncertain parameters, and disturbance. Reference [25] investigated the modified function projective lag synchronization of dynamical complex networks with disturbance, unknown parameters, and coupling delay based on error feedback control scheme. In [26], Du et al achieved the function projective synchronization for general complex dynamical networks with constant or time-varying time-delay coupling by a hybrid feedback control method, but the model uncertain and external disturbances were not taken into account. When the reference node is a chaotic attractor, the idea mentioned in this paper can synchronize complex network with a chaotic state, which can be applied in engineering fields such as secure communication and information processing.
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