Structure of the Phase Portrait of a Piecewise-Linear Dynamical System

N. B. Ayupova; V. P. Golubyatnikov

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Structure of the Phase Portrait of a Piecewise-Linear Dynamical System

机译：分段线性动力系统相位肖像的结构

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We consider some piecewise linear 4-dimensional dynamical system that models a gene network regulated by one negative feedback and three positive feedbacks. Glass and Pasternack described the conditions for the existence of a stable cycle in this model. We construct an invariant piecewise linear surface with nontrivial link with the Glass-Pasternack cycle outside the attraction domain of this stable cycle in the phase portrait of this system.

机译：我们考虑了一些分段线性4维动力系统，其模拟了一个负反馈的基因网络和三个正反馈。玻璃和pasternack描述了该模型中存在稳定循环的条件。我们构造了一个不变的分段线性表面，与该系统的相位肖像中这种稳定循环的吸引域外的玻璃瓶循环的非玻璃包装循环。

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来源
《Journal of applied and industrial mathematics》 |2019年第4期|共6页
作者
N. B. Ayupova; V. P. Golubyatnikov;
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作者单位

1grid.426295.e0000 0004 0620 109XSobolev Institute of Mathematicspr. Akad. Koptyuga 4630090NovosibirskRussia;

1grid.426295.e0000 0004 0620 109XSobolev Institute of Mathematicspr. Akad. Koptyuga 4630090NovosibirskRussia;

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原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
block-linear dynamical system; phase portrait; invariant surface; cycle; Poincaré mapping; gene network model; Hopf link;

机译：块线性动力系统;相位肖像;不变表面;循环;Poincaré映射;基因网络模型;HOPF链接;

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1. Structure of the Phase Portrait of a Piecewise-Linear Dynamical System [J] . N. B. Ayupova, V. P. Golubyatnikov Journal of applied and industrial mathematics . 2019,第4期

机译：分段线性动力系统相位肖像的结构
2. GOOD REDUCTION AND SHAFAREVICH-TYPE THEOREMS FOR DYNAMICAL SYSTEMS WITH PORTRAIT LEVEL STRUCTURES [J] . Silverman Joseph H. Pacific journal of mathematics . 2018,第1期

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3. A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems [J] . Roulet Javier, Mindlin Gabriel B. International journal of bifurcation and chaos in applied sciences and engineering . 2017,第13期

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4. On the separability of the parameter space of dynamical systems in terms of types of phase portraits [C] . Nagiev Ali, Imranov Fariz, Nagiev Hasan 2012 4th International Conference "Problems of Cybernetics and Informatics". . 2012

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5. Application of semiempirical electronic structure methods to studies of structures and dynamics of molecular clusters and condensed phase systems. [D] . Yu, Ning. 2003

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7. Structure of the phase portrait of a piecewise-linear dynamical system [O] . N. B. Ayupova, V. P. Golubyatnikov 2019

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8. Phase Equilibria, Thermodynamics, and Crystal Structures for the Pu-Pt-Rh System [R] . D. E. Peterson, C. C. Land, R. B. Roof 1977

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Structure of the Phase Portrait of a Piecewise-Linear Dynamical System

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