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| 1 | Comparative study on bifurcation control methods in a fractional-order delayed predator-prey system显示文摘This paper focuses on the comparative analysis of bifurcation control approaches for a fractional-order delayed predator-prey system. The state feedback schemes with and without time delay are dexterously designed during the bifurcation control for the proposed system, and the comparative study is elaborately performed on bifurcation control theoretically. The salient feature of the current paper is that the analysis of time of bifurcation control for the proposed system is investigated based on various state feedback control strategies. Analysis reveals that the feedback control approach without time delay overly outmatches the one with time delay for bifurcation control in the considered systems so long as the uniform feedback gain is selected. It consumes less time to control bifurcation while utilizing the first controller in comparison with the second one. Numerical examples are ultimately employed to confirm the correctness of the theoretical results. | HUANG ChengDai CAO JinDe | 2019 | Science China(Technological Sciences)2019，62，2： | 3 |
| 2 | Positivity and Stability of Fractional-Order Linear Time-Delay Systems显示文摘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)subsystems.Firstly,a sufficient and necessary condition is given to ensure the positivity of FOLTDSs.The 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 time-delays.Secondly,a theorem is given to prove the asymptotic stability of positive FOLTDSs.By 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 time-delay.Next,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 convergent.When 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 presented.Finally,simulation examples are presented to verify the validity and practicability of the theoretical analysis. | HAO Yilin HUANG Chengdai CAO Jinde LIU Heng | 2022 | Journal of Systems Science & Complexity2022，35，6： | 1 |
| 3 | Improving dynamics of integer-order small-world network models under fractional-order PD control显示文摘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. | Huaifei WANG Min XIAO Binbin TAO Fengyu XU Zhengxin WANG Chengdai HUANG Jianlong QIU | 2020 | Science China(Information Sciences)2020，63，1： | 1 |
| 4 | Stability and bifurcation analysis of a fractional-order single-gene regulatory model with delays under a novel PD^α control law显示文摘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 delays.The 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 model.It is demonstrated that the fractional-order gene regulatory model becomes controllable by adjusting the control gain parameters.In addition,the effect of fractional-order parameter on the dynamical behaviors is shown.Finally,numerical simulations are carried out to testify the validity of the main results and the availability of the fractional-order PD controller. | Qiu Lu Min Xiao Zunshui Cheng Yurong Song Chengdai Huang Jinde Cao | 2020 | International Journal of Biomathematics2020，13，3： | 0 |
| 5 | Novel method to detect Hopf bifurcation in a delayed fractional-order network model with bidirectional ring structure显示文摘In this paper,we formulate and study a fractional-order network model with four neurons,bidirectional ring structure and self-delay feedback.For 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 interval.For the scenario of identical neurons,we apply the crossing curves method to the fractional functional equations and thus procure the Hopf bifurcation curve.The 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 direction.Finally,we deliberate on the correctness of our methodology through two demonstration examples. | Shuai Li Chengdai Huang Xinyu Song | 2023 | International Journal of Biomathematics2023，16，6： | 0 |
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