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Bifurcation Analysis of a Neutrophil Periodic Oscillation Model with State Feedback Control

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International Journal of Modern Nonlinear Theory and Application 2023年第1期12卷 1-17页

作者： suqi ma Department of mathematics China Agricultural University Beijing China

The mathematical model of stem cells is discussed with its motivation to describe the tissue relationship by technically introducing a two compartments model. The clear link between the proliferation phase of stem cells and the circulating neutrophil phase is set forth after delay feedback control of the state variable of stem cells. Hopf bifurcation is discussed with varying free parameters and time delays. Based on the center manifold theory, the normal form near the critical point is computed and the stability of bifurcating periodical solution is rigorously discussed. With the aids of the artificial tool on-hand which implies how much tedious work doing by DDE-Biftool software, the bifurcating periodic solution after Hopf point is continued by varying time delay.

关键词： Neutrophil Phase Time Delay Hopf Bifurcation DDE-Biftool Fold Periodical Bifurcation Period-Doubling Bifurcation

Periodical Bifurcation Analysis of a Type of Hematopoietic Stem Cell Model with Feedback Control

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International Journal of Modern Nonlinear Theory and Application 2023年第1期12卷 18-29页

作者： suqi ma Department of mathematics China Agricultural University Beijing China

The delay feedback control brings forth interesting periodical oscillation bifurcation phenomena which reflect in mackey-Glass white blood cell model. Hopf bifurcation is analyzed and the transversal condition of Hopf bifurcation is given. Both the period-doubling bifurcation and saddle-node bifurcation of periodical solutions are computed since the observed floquet multiplier overpass the unit circle by DDE-Biftool software in matlab. The continuation of saddle-node bifurcation line or period-doubling curve is carried out as varying free parameters and time delays. Two different transition modes of saddle-node bifurcation are discovered which is verified by numerical simulation work with aids of DDE-Biftool.

关键词： Bifurcation Saddle-Node Bifurcation Period-Doubling Bifurcation Hopf Bifurcation Time Delay

Turing Instability of Gray-Scott Reaction-Diffusion Model with Time Delay Effects

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International Journal of Modern Nonlinear Theory and Application 2023年第2期12卷 55-67页

作者： suqi ma Department of mathematics China Agricultural University Beijing China

The reaction diffusion Gray-Scott model with time delay is put forward with the assumption of Neumann boundary condition is satisfied. Based on the Turing bifurcation condition, the Turing curves on two parameter plane are discussed without time delay. The normal form is computed via applying Lyapunov-Schmidt reduction method in system of PDE, and the bifurcating direction of pitchfork bifurcation underlying codimension-1 singularity of Turing point is computed. The continuation of Pitchfork bifurcation is simulated with varying free parameter continuously near the turing point, which is in coincidence with the theoritical analysis results. The wave pattern formation in the case of turing instability is also simulated which discover Turing oscillation phenomena from periodicity to irregularity.

关键词： Reaction Diffusion Turing Bifurcation Normal Form Time Delay

Triple-Zero Bifurcation of Van Der Pol Oscillator with Delay Feedback

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International Journal of Modern Nonlinear Theory and Application 2021年第3期10卷 106-118页

作者： suqi ma Department of mathematics China Agricultural University Beijing China

A van der Pol equation underlying state feedback control is investigated and the triple-zero bifurcation arises at the bifurcation point which is of codimension three singularity. By applying Schmidt-Lyapunov reduction method combined with center manifold analytical technique, the near approximating formal norm is derived at the triple-zero point. Hence after, as varying parameters continuously, the numerical simulation produces homoclinic bifurcation solutions appearing in system. In addition, the numerical simulation also exhibits the produced double-period limit cycle with chosen bifurcation parameters and the routes to chaos via period-doubling bifurcation are also verified.

关键词： Triple-Zero Bifurcation Homoclinic Solutions DDEs

Stability and Bifurcation Analysis of a Type of Hematopoietic Stem Cell Model

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International Journal of Modern Nonlinear Theory and Application 2021年第1期10卷 13-27页

作者： suqi ma Department of mathematics China Agricultural University Beijing China

The observed dynamical property illustrates that state feedback control may stabilize invariant attractor to stable state in a simple version of hematopoietic stem cell model. The stability character of the positive steady state is analyzed by the computation of the rightmost characteristic roots in complex plane. Hopf bifurcation points are tracked as the roots curve crossing imaginary axis from the left half plane to the right half plane continuously. The bifurcation direction and stability of the bifurcating periodical solution are discussed by norm form computation combined with the center manifold theory. Furthermore, the numerical simulation verifies that instead of chaos, system is stabilized to period-1, 2, 3, 4 and period-7 periodical solutions in some delay windows, and the continuous of periodical solutions is also numerical simulated with varying free parameters continuously.

关键词： State Feedback Control Time Delay Hopf Bifurcation

Periodic Oscillation in Neutrophil Models with Time Delays

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International Journal of Modern Nonlinear Theory and Application 2017年第4期6卷 119-133页

作者： suqi ma mathematical Department College of Science China Agricultural University Beijing China

To understand dynamical characters of neutrophil dynamical behavior, the sensitivity of delay factors which has effects on system dynamic behavior is ubiquitous due to system’s highly nonlinearity. Here we prove that delay supports a subcritical Hopf bifurcation, underlying a feedback mechanism during stem cells proliferation process while changing its coefficient of amplification. The given cell model reproduces a bistable dynamic regime of blood cells and hysteresis. Applying multiple scale method, oscillation motion near Hopf point is discussed. The stability limit of steady state to be abruptly periodic solution is detected.

关键词： Bautin Bifurcation Time Delay Neutrophil Dynamics

Two-Dimensional manifolds with Computation V-Function of ODE Systems

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International Journal of Modern Nonlinear Theory and Application 2023年第4期12卷 99-106页

作者： suqi ma Bohan ma Xinping Wang Department of mathematics China Agricultural University Beijing China Department of Mechanics Southwest Jiaotong University Chengdu China

The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too.

关键词： Stable manifold Unstable manifold V-Function Attraction Boundary

具有非线性出生率的时滞Lasota-Wazewska模型的稳定性分岔

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南京师大学报（自然科学版） 2005年第2期28卷 1-5页

作者：马苏奇陆启韶北京航空航天大学理学院

研究了一类Lasota-Wazewska单种群人口模型x′(t)=-μx(t)+pe-dτe-γx(t-τ).其中的出生率是时滞τ的非线性函数pe-dτ而不是常数p.应用选择性的方法或中心流形定理,确定了分岔周期解的稳定性及Hopf分岔的方向.应用计算机软件和数值方... 详细信息

研究了一类Lasota-Wazewska单种群人口模型x′(t)=-μx(t)+pe-dτe-γx(t-τ).其中的出生率是时滞τ的非线性函数pe-dτ而不是常数p.应用选择性的方法或中心流形定理,确定了分岔周期解的稳定性及Hopf分岔的方向.应用计算机软件和数值方法,也得到了一些相图和轨线的时间历程图.

关键词： Lasota-Wazewska模型成熟时滞 Hopf分岔

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针灸补脾疗法治疗糖尿病前期疗效观察

反射疗法与康复医学 2020年第18期1卷 46-48页

作者：马素起青岛市第五人民医院山东青岛266002

目的评价针灸穴位补脾疗法治疗糖尿病前期的疗效.方法选取2018年1月—2019年11月青岛市第五人民医院收治的88例糖尿病前期患者,随机分为观察组(44例)和对照组(44例),观察组患者采用针灸穴位补脾疗法,对照组患者采用单纯生活方式干预,比... 详细信息

目的评价针灸穴位补脾疗法治疗糖尿病前期的疗效.方法选取2018年1月—2019年11月青岛市第五人民医院收治的88例糖尿病前期患者,随机分为观察组(44例)和对照组(44例),观察组患者采用针灸穴位补脾疗法,对照组患者采用单纯生活方式干预,比较不同干预方法的效果.结果观察组经治疗后满意度评分为(92.16±1.34)分,高于对照组的(78.25±2.04)分,差异有统计学意义(P0.05);治疗后,两组患者的糖耐量受损情况均得到一定改善,但观察组的改善效果明显优于对照组,差异有统计学意义(P<0.05).结论采用针灸穴位补脾疗法对糖尿病前期患者进行治疗能够综合提高患者的满意度,提升整体的治疗有效率,改善糖耐量受损情况,是值得推广应用的一种治疗手段.

关键词：针灸穴位补脾疗法糖尿病前期治疗效果中医治疗穴位手法