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Stability switches and bifurcation analysis in a coupled neural system with multiple delays

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Science China(Technological Sciences) 2016年第6期59卷 920-931页

作者： GE Ju Hong XU Jian Department of Mathematics and Information Science Henan University of Economics and Law School of Aerospace Engineering and Applied Mechanics Tongji University

A coupled neural system with multiple delays has been investigated. The number of equilibrium points is analyzed. It implies that the neural system exhibits a unique equilibrium and three ones for the different values of coupling weight by employing the pitchfork bifurcation of the trivial equilibrium point. Further, the local asymptotical stability of the trivial equilibrium point is studied by analyzing the corresponding characteristic equation. Some stability criteria involving multiple delays and coupling weight are obtained. The results show that the neural system exhibits the delay-independent and delay-dependent stability. Increasing delay induces stability switching between resting state and periodic motion in some parameter regions of coupling weight. In addition, the criterion for the global stability of the trivial equilibrium is also derived by constructing a suitable Lyapunov functional. Finally, some numerical simulations are taken to support the theoretical results.

关键词： multiple delays stability switches global stability

Variable-step integration method for milling chatter stability prediction with multiple delays

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Science China(Technological Sciences) 2011年第12期54卷 3137-3154页

作者： ZHANG XiaoJian XIONG CaiHua DING Ye XIONG YouLun State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan 430074 China State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong University Shanghai 200240 China

This paper analyzes the stability of milling with variable pitch cutter and tool runout cases characterized by multiple delays,and proposes a new variable-step numerical integration method for efficient and accurate stability prediction. The variable-step technique is emphasized here to expand the numerical integration method,especially for the low radial immersion cases with multiple delays. First,the calculation accuracy of the numerical integration method is discussed and the variable-step algorithm is developed for milling stability prediction for single-delay and multiple-delay cases,respectively. The milling stability with variable pitch cutter is analyzed and the result is compared with those predicted with the frequency domain method and the improved full-discretization method. The influence of the runout effect on the stability boundary is investigated by the presented method. The numerical simulation shows that the cutter runout effect increases the stability boundary,and the increasing stability limit is verified by the milling chatter experimental results in the previous research. The numerical and experiment results verify the validity of the proposed method.

关键词： variable-step numerical integration method milling chatter stability prediction multiple delays variable pitch cutter cutter runout

Stability and Bifurcation Analysis in a System of Four Coupled Neurons with multiple delays

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 425-448页

作者： Xiu-ling LI Jun-jie WEI College of Applied Mathematics Jilin University of Finance and Economics Department of Mathematics Harbin Institute of Technology

A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability and bifurcation of the system are studied in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements. Meanwhile, the bifurcation set are drawn in the parameter space.

关键词： stability bifurcation multiple delays

Stability switches and Bogdanov-Takens bifurcation in an inertial two-neuron coupling system with multiple delays

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Science China(Technological Sciences) 2014年第5期57卷 893-904页

作者： SONG ZiGen XU Jian College of Information Technology Shanghai Ocean University School of Aerospace Engineering and Applied Mechanics Tongji University

In this paper,we investigate an inertial two-neural coupling system with multiple *** analyze the number of equilibrium points and demonstrate the corresponding pitchfork *** show that the system has a unique equilibrium as well as three equilibria for different values of coupling *** local asymptotic stability of the equilibrium point is studied using the corresponding characteristic *** find that multiple delays can induce the system to exhibit stable switching between the resting state and periodic *** regions with delay-dependence are exhibited in the parameter plane of the time delays employing the Hopf bifurcation *** obtain the global perspective of the system dynamics,stability and periodic activity involving multiple equilibria are investigated by analyzing the intersection points of the pitchfork and Hopf bifurcation curves,called the Bogdanov-Takens(BT)*** homoclinic bifurcation and the fold bifurcation of limit cycle are obtained using the BT theoretical results of the third-order normal ***,numerical simulations are provided to support the theoretical analyses.

关键词： inertial two-neuron system multiple delays stability switches Bogdanov-Takens bifurcation multiple stability

Bifurcation behaviors analysis of a plankton model with multiple delays

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International Journal of Biomathematics 2016年第6期9卷 113-137页

作者： Anuj Kumar Sharma Amit Sharma Kulbhushan Agnihotri Department of Mathematics LRDA V College Jagraon Punjab India DA V Institute of Engineering and Technology Jalandhar Punjab 144001 India Applied Science Department SBSSTC Ferozpur Punjab India

A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.

关键词： Plankton multiple delays toxin Hopf bifurcation normal form theory centermanifold theorem.

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEM WITH multiple delays

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Applied Mathematics and Mechanics(English Edition) 2003年第1期24卷 117-122页

作者： CAOXian－bing BasicSciencesDepartment BeijingTechnologyandBusinessUniversityBeijing100037China

The existence of T-periodic solutions of the nonlinear system with multiple delaysis studied. By using the topological degree method, sufficient conditions are obtained forthe existence of T-periodic solutions. As an application, the existence of positive periodicsolution for a logarithmic population model is established under some conditions.

关键词： multiple delays periodic solution topological degree

Stability Analysis of n-Dimensional Neutral Diferential Equations with multiple delays

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Journal of Mathematical Research with Applications 2013年第6期33卷 631-652页

作者： Xianfeng ZHOU Wei JIANG Lianggen HU School of Mathematical Sciences Anhui University Department of Mathematics Ningbo University

This paper is mainly concerned with stability analysis of neutral diferential equations with multiple *** criteria on instability,stability,asymptotic stability and exponential stability are *** criterion on asymptotic stability is necessary and *** examples are provided to illustrate the applications of our *** previous results are extended.

关键词： stability analysis neutral diferential equation multiple delays

Synchronization Stability in an Array of Linearly Coupled Connected Neural Networks with multiple delays

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Synchronization Stability in an Array of Linearly Coupled Co...

Novel synchronization criteria for a class of neural networks with multiple delays

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作者： Zhanshan Wang, Dakai Zhou, Dawei Gong, Xiangnan Zhong School of Information Science and Engineering, Northeastern University, Shenyang, 110004

In this paper, synchronization stability problem for arrays of linearly coupled multiple delayed neural net- works is studied on the basis of LMI method. The derived results greatly improve and generalize some earlier results. Some key problems between stability of recurrent neural networks and synchronization stability of arrays of coupled neu- ral networks are discussed in some Remarks. A numerical example is used to illustrate the effectiveness of the derived results.

关键词： Synchronization stability arrays of coupled neural networks multiple delays global stability

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Novel synchronization criteria for a class of neural network...