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Positivity and Stability of Fractional-Order Linear Time-Delay Systems

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Journal of Systems Science & Complexity 2022年第6期35卷 2181-2207页

作者： HAO Yilin huang chengdai CAO Jinde LIU Heng School of Mathematics and Physics Guangxi University for NationalitiesNanning 530006China School of Mathematics and Statistics Xinyang Normal UniversityXinyang 464000China School of Mathematics Southeast UniversityNanjing 211189China

This article focuses on the positivity and the asymptotic stability of fractional-order linear time-delay systems(FOLTDSs)which are composed of N(N≥2)***,a sufficient and necessary condition is given to ensure the positivity of *** solutions of the studied systems are obtained by using the Laplace transform method,and it can be observed that the positivity of FOLTDSs is completely determined by the series of matrices and independent of the magnitude of ***,a theorem is given to prove the asymptotic stability of positive *** considering the monotonicity and asymptotic properties of systems with constant time-delay,it is further shown that the asymptotic stability of positive FOLTDSs is independent of the ***,a state-feedback controller,whose gain matrix is derived by resolving a linear programming question,is designed such that the state variables of the systems are nonnegative and asymptotically *** the order of the FOLTDSs is greater than one,by utilizing a proposed property of Caputo derivative,a sufficient condition for the positivity of FOLTDS is ***,simulation examples are presented to verify the validity and practicability of the theoretical analysis.

关键词： Asymptotic stability fractional-order system linear programming positivity time-delay

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Novel method to detect Hopf bifurcation in a delayed fractional-order network model with bidirectional ring structure

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International Journal of Biomathematics 2023年第6期16卷 209-232页

作者： Shuai Li chengdai huang Xinyu Song School of Mathematics and Statistic Xinyang Normal University Xinyang 464000 P.R.China

In this paper,we formulate and study a fractional-order network model with four neurons,bidirectional ring structure and self-delay *** the scenario of nonidentical neurons,we develop a new algebraic technique to deal with the characteristic equation with e-4st(T is the self-feedback delay)term and thus establish the easy-tocheck criteria to determine the Hopf bifurcation point of self-feedback delay by fixing communication delay in its stable *** the scenario of identical neurons,we apply the crossing curves method to the fractional functional equations and thus procure the Hopf bifurcation *** obtained results accommodate the fact that the model cannot preserve its stability behavior when the self-feedback delay crosses the Hopf bifurcation point in the positive ***,we deliberate on the correctness of our methodology through two demonstration examples.

关键词： Neural networks delays crossing curves fractional order Hopf bifurcation

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分数阶时滞金融混沌系统的完全同步

信阳师范大学学报(自然科学版) 2025年第1期38卷 87-91页

作者：黄承代汪华南刘恒信阳师范大学数学与统计学院河南信阳464000 广西民族大学数学与物理学院广西南宁530006

讨论了一类新型的分数阶时滞金融混沌系统的完全同步问题。在响应系统中设计了3个包含时滞的反馈增益控制器,基于分数阶拉兹密辛定理并利用分数阶不等式,得到了一个保证驱动-响应系统完全同步的充分条件。结果表明,控制器的加入使得响... 详细信息

讨论了一类新型的分数阶时滞金融混沌系统的完全同步问题。在响应系统中设计了3个包含时滞的反馈增益控制器,基于分数阶拉兹密辛定理并利用分数阶不等式,得到了一个保证驱动-响应系统完全同步的充分条件。结果表明,控制器的加入使得响应系统的状态最终都会与驱动系统的状态保持完全同步,且误差系统的状态都将趋于稳定的状态。这说明控制器的设计是行之有效的。最后,给出了数值模拟以验证所得结果的正确性。

关键词：分数阶时滞金融混沌系统完全同步分数阶拉兹密辛定理

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Improving dynamics of integer-order small-world network models under fractional-order PD control

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Science China(Information Sciences) 2020年第1期63卷 200-212页

作者： Huaifei WANG Min XIAO Binbin TAO Fengyu XU Zhengxin WANG chengdai huang Jianlong QIU College of Automation Nanjing University of Posts and Telecommunications School of Mathematics and Physics Qingdao University of Science and Technology College of Science Nanjing University of Posts and Telecommunications School of Mathematics and Statistics Xinyang Normal University School of Automation and Electrical Engineering Linyi University

The optimal control of dynamics is a popular topic for small-world networks. In this paper, we address the problem of improving the behavior of Hopf bifurcations in an integer-order model of small-world networks. In this study, the time delay is used as the bifurcation parameter. We add a fractional-order proportional-derivative(PD) scheme to an integer-order Newman-Watts(N-W) small-world model to better control the Hopf bifurcation of the model. The most important contribution of this paper involves obtaining the stability of the system and the variation of the conditions of the Hopf bifurcation after a fractional PD controller is added to the integer-order small-world model. The results demonstrate that the designed PD controller can be used to restrain or promote the occurrence of Hopf bifurcations by setting appropriate parameters. We also describe several simulations to verify our research results.

关键词： small-world networks stability Hopf bifurcation bifurcation control fractional-order PD control

Stability and bifurcation analysis of a fractional-order single-gene regulatory model with delays under a novel PD^α control law

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International Journal of Biomathematics 2020年第3期13卷 37-54页

作者： Qiu Lu Min Xiao Zunshui Cheng Yurong Song chengdai huang Jinde Cao College of Automation Nanjing University of Posts and Telecommunications Nanjing 210003 China School of Mathematics and Physics Qingdao University of Science and Technology Qingdao 266061 China School of Mathematics and Statistics Xinyang Normal University Xinyang 464000China School of Mathematics Southeast University Nanjing 210096China

In this paper,we propose a novel fractional-order proportional-derivative(PD)strategy to achieve the control of bifurcation of a fractional-order gene regulatory model with *** stability theory of fractional differential equations proved that with delays,some explicit conditions for the local asymptotical stability and Hopf bifurcation are given for the controlled fractional-order genetic *** is demonstrated that the fractional-order gene regulatory model becomes controllable by adjusting the control gain *** addition,the effect of fractional-order parameter on the dynamical behaviors is ***,numerical simulations are carried out to testify the validity of the main results and the availability of the fractional-order PD controller.

关键词： Hopf bifurcation fractional-order single-genetic regulatory network fractional-order PD controller time delay