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Almost Automorphic Solutions for quaternion-valued Hopfield Neural Networks with Mixed Time-Varying Delays and Leakage Delays

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Journal of Systems Science & Complexity 2020年第1期33卷 100-121页

作者： LI Yongkun MENG Xiaofang Department of Mathematics Yunnan UniversityKunming 650091China

This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage *** utilizing the exponential dichotomy of linear differential equations,Banach’s fixed point theorem and differential inequality techniques,the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural *** results are completely ***,the authors give an example to illustrate the feasibility of the results.

关键词： Almost automorphic solutions exponential stability Hopfield neural networks leakage delays quaternion-valued functions

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Existence and Uniqueness Results for quaternion-valued Nonlinear Impulsive Differential Systems

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Journal of Systems Science & Complexity 2018年第3期31卷 596-607页

作者： ZHU Jingwen SUN Jitao Department of Mathematics Tongji University Shanghai 200092 China College of Mathematics and Physics Jinggangshan University Jinggangshan 343009 China Institute for Intelligent Systems University of Johannesburg South Africa.

This paper studies the existence and uniqueness conditions for the quaternion-valued non-linear impulsive system. Firstly, a space of quaternion-valued piecewise functions is constructed and completeness of the space is also proved. Then by taking advantage of the Bielecki norm and fixed point theorem, existence and uniqueness criteria of quaternion-valued nonlinear impulsive system are obtained. At last, an example is given to illustrate our theoretical results.

关键词： Differential equations, existence and uniqueness, impulsive system quaternion-valued

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Mittag-Leffler stability analysis of multiple equilibrium points in impulsive fractional-order quaternion-valued neural networks

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Frontiers of Information Technology & Electronic Engineering 2020年第2期21卷 234-246页

作者： K.UDHAYAKUMAR R.RAKKIYAPPAN Jin-de CAO Xue-gang TAN Department of Mathematics Hhamthiar Universityf Coimbatore 641046India School of Mathematics Southeast UniversityNanjing 210096China School of Automation Southeast UniversityNanjing 210096China

In this study,we investigate the problem of multiple Mittag-Leffler stability analysis for fractional-order quaternion-valued neural networks(QVNNs)with *** the geometrical properties of activation functions and the Lipschitz condition,the existence of the equilibrium points is *** addition,the global Mittag-Leffler stability of multiple equilibrium points for the impulsive fractional-order QVNNs is investigated by employing the Lyapunov direct ***,simulation is performed to illustrate the effectiveness and validity of the main results obtained.

关键词： Mittag-Leffler stability Fractional-order quaternion-valued neural networks Impulse

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