A quasi-periodic gravity modulation to suppress chaos in a Lorenz system

被引：5

作者：

Joundy, Youssef ^{[1
]}

Rouah, Hamza ^{[1
]}

Taik, Ahmed ^{[1
,2
]}

机构：

[1] Univ Hassan II Casablanca, Lab Math & Applicat, FST Mohammadia, POB 146, Mohammadia 20650, Morocco

[2] Mohammed VI Polytehn Univ UM6P, Modeling Simulat & Data Anal, Ben Guerir, Morocco

来源：

INTERNATIONAL JOURNAL OF DYNAMICS AND CONTROL | 2021年 / 9卷 / 02期

关键词：

Chaos; Gravitational modulation; Lyapunov exponents; Runge-Kutta method; NATURAL-CONVECTION; STABILITY; EXPLOSION; DYNAMICS; MODELS; ROUTES;

D O I：

10.1007/s40435-020-00679-y

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This work is devoted to study the influence of quasi-periodic gravitational modulation on suppress chaos in a two-dimensional rectangular Newtonian fluid heated from below. The model consists of the heat equation coupled with the Navier-Stokes equation under the Boussinesq approximation. The problem is reduced to an autonomous system of ordinary differential equations by using the approximation on some Fourier modes. We solved these system by using the fourth-order Runge-Kutta method. A transition from periodic oscillatory convection to chaotic convection is identified for certain value of Rayleigh number and shape parameter in 3D Lorenz model. The results also show that the chaos can be suppressed by applied to a medium a quasi-periodic gravitational modulation for high and low Prandtl number in both Lorenz models 3D and 5D.

引用

页码：475 / 493

页数：19

共 30 条

[1] Influence of Natural Convection on the Heat Explosion in Porous Media [J].

Allali, K. ;

Joundy, Y. ;

Taik, A. ;

Volpert, V. .

COMBUSTION EXPLOSION AND SHOCK WAVES, 2017, 53 (02) :134-139

[2] Dynamics of Convective Thermal Explosion in Porous Media [J].

Allali, Karam ;

Joundy, Youssef ;

Taik, Ahmed ;

Volpert, Vitaly .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2020, 30 (06)

[3] Suppression of Chaos in Porous Media Convection under Multifrequency Gravitational Modulation [J].

Allali, Karam .

ADVANCES IN MATHEMATICAL PHYSICS, 2018, 2018

[4] Measuring mass and angular momentum of black holes with high-frequency quasi-periodic oscillations [J].

Aschenbach, B .

ASTRONOMY & ASTROPHYSICS, 2004, 425 (03) :1075-1082

[5] LOW-DIMENSIONAL CHAOS IN AN INSTANCE OF EPILEPSY [J].

BABLOYANTZ, A ;

DESTEXHE, A .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1986, 83 (10) :3513-3517

[6] Effect of quasiperiodic gravitational modulation on the stability of a heated fluid layer [J].

Boulal, Taoufik ;

Aniss, Said ;

Belhaq, Mohamed ;

Rand, Richard .

PHYSICAL REVIEW E, 2007, 76 (05)

[7] Nonlinear dynamics of two-dimensional convection in a vertically stratified slot with and without gravity modulation [J].

Christov, CI ;

Homsy, GM .

JOURNAL OF FLUID MECHANICS, 2001, 430 :335-360

[8] Quasi-Periodic Orbits in the Five-Dimensional Nondissipative Lorenz Model: The Role of the Extended Nonlinear Feedback Loop [J].

Faghih-Naini, Sara ;

Shen, Bo-Wen .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (06)

[9] On the dynamics of five- and six-dimensional Lorenz models [J].

Felicio, Carolini C. ;

Rech, Paulo C. .

JOURNAL OF PHYSICS COMMUNICATIONS, 2018, 2 (02)

[10] CONTROLLING CARDIAC CHAOS [J].

GARFINKEL, A ;

SPANO, ML ;

DITTO, WL ;

WEISS, JN .

SCIENCE, 1992, 257 (5074) :1230-1235

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