Abstract
This paper presents the function projective synchronization problem of neural networks with mixed time-varying delays and uncertainties asymmetric coupling. The function projective synchronization of this model via hybrid adaptive pinning controls and hybrid adaptive controls, composed of nonlinear and adaptive linear feedback control, is further investigated in this study. Based on Lyapunov stability theory combined with the method of the adaptive control and pinning control, some novel and simple sufficient conditions are derived for the function projective synchronization problem of neural networks with mixed time-varying delays and uncertainties asymmetric coupling, and the derived results are less conservative. Particularly, the control method focuses on how to determine a set of pinned nodes with fixed coupling matrices and strength values and randomly select pinning nodes. Based on adaptive control technique, the parameter update law, and the technique of dealing with some integral terms, the control may be used to manipulate the scaling functions such that the drive system and response systems could be synchronized up to the desired scaling function. Finally, numerical examples are given to illustrate the effectiveness of the proposed theoretical results.
Highlights
Neural networks are under extensive consideration because of their significant application in various fields such as image processing, pattern recognition, and associative memories because the switching speed of information processing and the inherent neuron communication is limited [1, 2]
This paper presents the function projective synchronization problem of neural networks with mixed time-varying delays and uncertainties asymmetric coupling
It is well know that the time delay is continually necessarily existent in neural networks because it might lead to inconstancy or considerably inferior performances
Summary
Neural networks are under extensive consideration because of their significant application in various fields such as image processing, pattern recognition, and associative memories because the switching speed of information processing and the inherent neuron communication is limited [1, 2]. In Gao et al [19] the generalized function projective synchronization of weighted cellular neural networks with multiple time-varying coupling delays was studied. Hybrid adaptive pinning control for FPS of neural networks with mixed timevarying delays and uncertainties asymmetric coupling is an interesting topic for investigating. Based on constructing a novel Lyapunov-Krasovskii functional, adaptive control technique, the parameter update law, and the technique of dealing with Jensen’s and Cauchy inequalities, some novel sufficient conditions for guaranteeing the existence of the FPS of neural networks with mixed time-varying delays and uncertainties asymmetric coupling are derived.
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