Projective Synchronization Analysis of Fractional-Order Neural Networks With Mixed Time Delays

Projective synchronization (PS) is a type of chaos synchronization where the states of slave system are scaled replicas of the states of master system. This paper studies the asymptotic projective synchronization (APS) between master–slave chaotic neural networks (NNs) with mixed time-delays and unmatched coefficients. Based on useful inequality techniques and constructing a suitable Lyapunov functional, some simple criteria are derived to ensure the APS of considered networks via designing a novel adaptive feedback controller. In addition, a numerical example and its MATLAB simulations are provided to check the feasibility of the obtained results. The main innovation of our work is that we dealt with the APS problem between two different chaotic NNs, while most of the existing works only concerned with the PS of chaotic systems with the same topologies. In addition, compared with the controllers introduced in the existing papers, the designed controller in this paper does not require any knowledge about the activation functions, which can be seen as another novelty of the paper.

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Adaptive observer-based projective synchronization for chaotic neural networks with mixed time delays

Chinese Journal of Physics ◽

10.1016/j.cjph.2016.04.015 ◽

2016 ◽

Vol 54 (2) ◽

pp. 285-297 ◽

Cited By ~ 12

Author(s):

S. Tourani ◽

Z. Rahmani ◽

B. Rezaie

Keyword(s):

Neural Networks ◽

Time Delays ◽

Adaptive Observer ◽

Projective Synchronization ◽

Chaotic Neural Networks ◽

Mixed Time Delays

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Projective synchronization adaptive control for different chaotic neural networks with mixed time delays

Optik ◽

10.1016/j.ijleo.2015.11.227 ◽

2016 ◽

Vol 127 (5) ◽

pp. 2551-2557 ◽

Cited By ~ 5

Author(s):

Yong-Qing Fan ◽

Ke-Yi Xing ◽

Yin-He Wang ◽

Li-Yang Wang

Keyword(s):

Neural Networks ◽

Adaptive Control ◽

Time Delays ◽

Projective Synchronization ◽

Chaotic Neural Networks ◽

Mixed Time Delays

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Generalized Projective Synchronization between Two Different Neural Networks with Mixed Time Delays

Discrete Dynamics in Nature and Society ◽

10.1155/2012/153542 ◽

2012 ◽

Vol 2012 ◽

pp. 1-19 ◽

Cited By ~ 3

Author(s):

Xuefei Wu ◽

Chen Xu ◽

Jianwen Feng ◽

Yi Zhao ◽

Xuan Zhou

Keyword(s):

Neural Networks ◽

Time Delays ◽

Lyapunov Stability Theory ◽

Projective Synchronization ◽

Nonlinear Coupling ◽

Nonlinear Feedback ◽

Nonlinear Controller ◽

Feedback Controllers ◽

Mixed Time Delays ◽

Generalized Projective Synchronization

The generalized projective synchronization (GPS) between two different neural networks with nonlinear coupling and mixed time delays is considered. Several kinds of nonlinear feedback controllers are designed to achieve GPS between two different such neural networks. Some results for GPS of these neural networks are proved theoretically by using the Lyapunov stability theory and the LaSalle invariance principle. Moreover, by comparison, we determine an optimal nonlinear controller from several ones and provide an adaptive update law for it. Computer simulations are provided to show the effectiveness and feasibility of the proposed methods.

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Mixed H∞ and passive projective synchronization for fractional-order memristor-based neural networks with time delays via adaptive sliding mode control

Modern Physics Letters B ◽

10.1142/s0217984917501603 ◽

2017 ◽

Vol 31 (14) ◽

pp. 1750160 ◽

Cited By ~ 6

Author(s):

Shuai Song ◽

Xiaona Song ◽

Ines Tejado Balsera

Keyword(s):

Neural Networks ◽

Sliding Mode Control ◽

Fractional Order ◽

Time Delays ◽

Closed Loop ◽

Sliding Mode ◽

Projective Synchronization ◽

Adaptive Sliding Mode Control ◽

Closed Loop System ◽

Mode Control

This paper investigates the mixed [Formula: see text] and passive projective synchronization problem for fractional-order (FO) memristor-based neural networks with time delays. Our aim is to design a controller such that, though the unavoidable phenomena of time delay and external disturbances is fully considered, the resulting closed-loop system is stable with a mixed [Formula: see text] and passive performance level. By combining sliding mode control and adaptive control methods, a novel adaptive sliding mode control strategy is designed for the synchronization of time-delayed FO dynamic networks. Via the application of FO system stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequalities. Based on the conditions, a desired controller which can guarantee the stability of the closed-loop system and also ensure a mixed [Formula: see text] and passive performance level is designed. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.

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