The Study of the Model Which Can Explain Somite Patterning in Embryos
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- 英文论文题名：The Study of the Model Which Can Explain Somite Patterning in Embryos
- 论文作者：Guan Linan ; Shen Jianwei
- 英文论文作者：Guan Linan ; Shen Jianwei ; School of Mathematics and Statistics ; Zhengzhou University
- 年：2016
- 作者机构：School of Mathematics and Statistics, Zhengzhou University;
- 英文论文关键词：HIV-1 infection model ; Virus dynamics ; Delays ; Stability analysis ; Hopf bifurcation
- 会议召开时间：2016-05-06
- 会议录名称：第十届动力学与控制学术会议摘要集
- 语种：英文
- 分类号：Q-33
- 学会代码：AGLU
- 会议名称：第十届动力学与控制学术会议
- 会议地点：中国四川成都
- 主办单位：中国力学学会动力学与控制专业委员会
- 学会名称：中国力学学会
- 页数：2
- 文件大小：746k
- 原文格式：D
- 会议级别：全国
摘要
Using a systematic computationalapproach and in vivo experiments,Cotterell et al. challenge a40-year-oldmodel that explains large-scaleembryonic patterns in terms of long-rangegradients. Instead, they show thatthese patterns can arise from short-rangeinteractions and that a modifiedreactiondiffusionmechanism can drive the self-organizationobservedduringsomitogenesis.Inthis paper,weinves-tigated the modified two dimensional model. Itis suitablefor exploring a design space of somitogenesisand can explain aspects of somitogenesis that previous models cannot. We mainly studied the non-diffusing case.We have used the Hopf bifurcation theorem,bifurcation theory and the Center manifold theorem in our investigation.Our model exhibits subcritical Hopf bifurcation for certain parameter values which marks the instability of limit cycles destroyed in Hopf bifurcations.And we get the condition in which the bistable state of the system exists.In addition to,we getan equation in terms of two parameters that tells us for what values of the parameterswe will havenon-hyperbolic fixed points(i.e.limit point bifurcation).Because somitogenesisin the process of biological development occupies an important position,and as a pattern process can be used to study pattern formation and many aspects of embryogenesis.So our study have a great help for Embryonic development,gene expression,cell differentiation.In addition to,it is beneficial to study the clone animal variation problem of spinal bone number.
Using a systematic computationalapproach and in vivo experiments,Cotterell et al. challenge a40-year-oldmodel that explains large-scaleembryonic patterns in terms of long-rangegradients. Instead, they show thatthese patterns can arise from short-rangeinteractions and that a modifiedreactiondiffusionmechanism can drive the self-organizationobservedduringsomitogenesis.Inthis paper,weinves-tigated the modified two dimensional model. Itis suitablefor exploring a design space of somitogenesisand can explain aspects of somitogenesis that previous models cannot. We mainly studied the non-diffusing case.We have used the Hopf bifurcation theorem,bifurcation theory and the Center manifold theorem in our investigation.Our model exhibits subcritical Hopf bifurcation for certain parameter values which marks the instability of limit cycles destroyed in Hopf bifurcations.And we get the condition in which the bistable state of the system exists.In addition to,we getan equation in terms of two parameters that tells us for what values of the parameterswe will havenon-hyperbolic fixed points(i.e.limit point bifurcation).Because somitogenesisin the process of biological development occupies an important position,and as a pattern process can be used to study pattern formation and many aspects of embryogenesis.So our study have a great help for Embryonic development,gene expression,cell differentiation.In addition to,it is beneficial to study the clone animal variation problem of spinal bone number.
Using a systematic computationalapproach and in vivo experiments,Cotterell et al. challenge a40-year-oldmodel that explains large-scaleembryonic patterns in terms of long-rangegradients. Instead, they show thatthese patterns can arise from short-rangeinteractions and that a modifiedreactiondiffusionmechanism can drive the self-organizationobservedduringsomitogenesis.Inthis paper,weinves-tigated the modified two dimensional model. Itis suitablefor exploring a design space of somitogenesisand can explain aspects of somitogenesis that previous models cannot. We mainly studied the non-diffusing case.We have used the Hopf bifurcation theorem,bifurcation theory and the Center manifold theorem in our investigation.Our model exhibits subcritical Hopf bifurcation for certain parameter values which marks the instability of limit cycles destroyed in Hopf bifurcations.And we get the condition in which the bistable state of the system exists.In addition to,we getan equation in terms of two parameters that tells us for what values of the parameterswe will havenon-hyperbolic fixed points(i.e.limit point bifurcation).Because somitogenesisin the process of biological development occupies an important position,and as a pattern process can be used to study pattern formation and many aspects of embryogenesis.So our study have a great help for Embryonic development,gene expression,cell differentiation.In addition to,it is beneficial to study the clone animal variation problem of spinal bone number.
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