Analysis of the multi-phenomenal nonlinear system : Testing Integrability and detecting chaos

被引：1

作者：

Benkhali, Mohamed ^{[1
]}

Kharbach, Jaouad ^{[1
]}

Hammouch, Zakia ^{[2
,3
,4
,5
]}

Chatar, Walid ^{[1
]}

El Ghamari, Mohammed ^{[1
]}

Rezzouk, Abdellah ^{[1
]}

Ouazzani-Jamil, Mohammed ^{[5
]}

机构：

[1] Univ Sidi Mohamed Ben Abdellah, Fac Sci Dhar El Mahraz, Lab Phys Solide, BP 1796, Fez Atlas 30000, Morocco

[2] Univ Moulay Ismail, Ecole Normale Super Meknes, Meknes, Morocco

[3] Thu Dau Mot Univ, Div Appl Math, Thu Dau Mot, Binh Duong Prov, Vietnam

[4] China Med Univ Hosp, Dept Med Res, Taichung, Taiwan

[5] Univ Privee Fes, Lab Syst & Environm Durables, Lot Quaraouiyine Route Ain Chkef, Fes, Morocco

来源：

RESULTS IN PHYSICS | 2023年 / 47卷

关键词：

Multi-phenomenal nonlinear system; Painlev? analysis; Integrability; Integrals of motion; Smaller Alignment Index; Poincar? Section Surface; Maximum Lyapunov Exponent; ORDINARY DIFFERENTIAL-EQUATIONS; FAST LYAPUNOV INDICATOR; PHASE-SPACE STRUCTURE; HAMILTONIAN-SYSTEMS; SYMPLECTIC MAPPINGS; EVOLUTION-EQUATIONS; DYNAMICAL-SYSTEMS; SOLAR-SYSTEM; PAINLEVE; ORBITS;

D O I：

10.1016/j.rinp.2023.106346

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

As a large extension in Hamiltonian form, the system of a PT symmetric dimer of coupled nonlinear oscillators is developed. This system provides an explanation for a number of problems with Hamiltonian dynamics. Integrability is evaluated in the Painleve sense of the system. The system reported twelve P-cases. First integrals of planar motion are constructed explicitly for each integrable case to show the Liouvillian integrability of the equations of motion. A mixture of numerical approaches is used to test the theoretical conclusions in order to identify the nature of orbits and evaluate the system's transition from order to chaos. These techniques consist of the Poincare Section Surface, the maximum Lyapunov Exponent, and the Smaller Alignment Index.

引用

页数：14

共 71 条

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