Periodicity of the Lorenz-Stenflo equations

Park Junho; Lee Hyunho; Jeon Ye-Lim; Baik Jong-Jin

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Periodicity of the Lorenz-Stenflo equations

机译：Lorenz-Stenflo方程的周期性

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摘要

In this paper, we investigate periodic behaviors of the Lorenz-Stenflo equations in wide ranges of parameters. Regimes of periodic solutions and chaotic solutions are computed and distinguished by local maximum values of a dynamic variable Z. Complex behaviors of the periodic solutions are observed inside a regime of the chaotic solutions which is closed and surrounded by a regime of the periodic solutions where a feature of disconnected bifurcations is observed. It is found that not only a regime of fixed solutions but also regimes of solutions with period 1 and 2 remain for sufficiently large parameters.

机译：在本文中，我们研究了Lorenz-Stenflo方程在宽范围参数中的周期性行为。通过动态变量Z的局部最大值来计算和区分周期解和混沌解的形式。在混沌解的一个状态内观察到周期解的复杂行为，该混沌解被一个周期解的状态所封闭和包围。观察到不连续分叉的特征。已经发现，对于足够大的参数，不仅保留了固定解的状态，而且还保留了周期为1和2的解的状态。

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《Physica Scripta: An International Journal for Experimental and Theoretical Physics》 |2015年第6期|共5页
作者
Park Junho; Lee Hyunho; Jeon Ye-Lim; Baik Jong-Jin;
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正文语种 eng
中图分类物理学;
关键词
Lorenz-Stenflo equations; periodicity; chaos; nonlinear dynamics;

机译：Lorenz-Stenflo方程;周期;混沌;非线性动力学;

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1. Stability and periodicity of high-order Lorenz-Stenflo equations [J] . Park Junho, Han Beom-Soon, Lee Hyunho, Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2016,第6期

机译：高阶Lorenz-Stenflo方程的稳定性和周期性
2. Spiral organization of periodic structures in the Lorenz-Stenflo system [J] . Rech Paulo C. Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2016,第7期

机译：Lorenz-Stenflo系统中周期性结构的螺旋组织
3. Periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent and Poisson stable solutions for stochastic differential equations [J] . Journal of Differential Equations . 2020,第4期

机译：周期性，准周期性，几乎定期的，几乎同时的随机微分方程的泊松稳定和泊松稳定解决方案
4. On Periodic Solutions of Singularly Perturbed Integro-differential Volterra Equations with Periodic Nonlinearities [C] . Vera B. Smirnova, Natalia V. Utina, Anton V. Proskurnikov IFAC Workshop on Periodic Control Systems . 2016

机译：定期扰动积分差分Volterra方程与周期性非线性的周期解
5. Analysis of partial differential equations with time-periodic forcing, applications to Navier-Stokes equations. [D] . Coros, Corina Alexandra. 2006

机译：带有时间周期强迫的偏微分方程分析，应用于Navier-Stokes方程。
6. Periodicity computation of generalized mathematical biology problems involving delay differential equations [O] . M. Jasim Mohammed, Rabha W. Ibrahim, M.Z. Ahmad 2017

机译：含时滞微分方程的广义数学生物学问题的周期性计算
7. Survey of Periodic Solutions of the Nonlinear Ordinary Differential Equations and Study of Periodic Solutions of the Duffing Type Equation with the Square Wave External Force (Progress in Qualitative Theory of Functional Equations) [O] . Nohara Ben T., Arimoto Akio 2012

机译：非线性常微分方程的周期解的研究以及具有方波外力的Duffing型方程的周期解的研究（功能方程定性理论的进展）
8. PART I Recent Work on Families of Periodic Solutions of Ordinary Differential Equations. PART II Singular Solutions of Systems of Real Analytic Equations. PART III The Stromgren-Wintner Principle on the Termination of Families of Periodic Solutions. [R] . Daniel C. Lewis 1959

机译：第一部分关于常微分方程周期解族的近期研究。第二部分实分析方程组的奇异解。第三部分stromgren-Wintner关于终止家庭周期解的原则。

Periodicity of the Lorenz-Stenflo equations

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