Singular Orbits and Dynamics at Infinity of a Conjugate Lorenz-Like System
A conjugate Lorenz-like system which includes only two quadratic nonlinearities is proposed in this paper. Some basic properties of this system, such as the distribution of its equilibria and their stabilities, the Lyapunov exponents, the bifurcations are investigated by some numerical and theoretic...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2015-03-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/991 |
| _version_ | 1818566084458971136 |
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| author | Fengjie Geng Xianyi Li |
| author_facet | Fengjie Geng Xianyi Li |
| author_sort | Fengjie Geng |
| collection | DOAJ |
| description | A conjugate Lorenz-like system which includes only two quadratic nonlinearities is proposed in this paper. Some basic properties of this system, such as the distribution of its equilibria and their stabilities, the Lyapunov exponents, the bifurcations are investigated by some numerical and theoretical analysis. The forming mechanisms of compound structures of its new chaotic attractors obtained by merging together two simple attractors after performing one mirror operation are also presented. Furthermore, some of its other complex dynamical behaviours, which include the existence of singularly degenerate heteroclinic cycles, the existence of homoclinic and heteroclinic orbits and the dynamics at infinity, etc, are formulated in detail. In the meantime, some problems deserving further investigations are presented. |
| first_indexed | 2024-12-14T01:49:12Z |
| format | Article |
| id | doaj.art-47299ffc95f64d92a5d4584e2d227c78 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-14T01:49:12Z |
| publishDate | 2015-03-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-47299ffc95f64d92a5d4584e2d227c782022-12-21T23:21:26ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102015-03-0120210.3846/13926292.2015.1019944Singular Orbits and Dynamics at Infinity of a Conjugate Lorenz-Like SystemFengjie Geng0Xianyi Li1School of Science, China University of Geosciences (Beijing), 100083 Beijing, ChinaCollege of Mathematical Science, Yangzhou University, 225002 Yangzhou, ChinaA conjugate Lorenz-like system which includes only two quadratic nonlinearities is proposed in this paper. Some basic properties of this system, such as the distribution of its equilibria and their stabilities, the Lyapunov exponents, the bifurcations are investigated by some numerical and theoretical analysis. The forming mechanisms of compound structures of its new chaotic attractors obtained by merging together two simple attractors after performing one mirror operation are also presented. Furthermore, some of its other complex dynamical behaviours, which include the existence of singularly degenerate heteroclinic cycles, the existence of homoclinic and heteroclinic orbits and the dynamics at infinity, etc, are formulated in detail. In the meantime, some problems deserving further investigations are presented.https://journals.vgtu.lt/index.php/MMA/article/view/991Hopf bifurcationsingularly degenerate heteroclinic cyclehomoclinic and heteroclinic orbitsPoincare compactification |
| spellingShingle | Fengjie Geng Xianyi Li Singular Orbits and Dynamics at Infinity of a Conjugate Lorenz-Like System Mathematical Modelling and Analysis Hopf bifurcation singularly degenerate heteroclinic cycle homoclinic and heteroclinic orbits Poincare compactification |
| title | Singular Orbits and Dynamics at Infinity of a Conjugate Lorenz-Like System |
| title_full | Singular Orbits and Dynamics at Infinity of a Conjugate Lorenz-Like System |
| title_fullStr | Singular Orbits and Dynamics at Infinity of a Conjugate Lorenz-Like System |
| title_full_unstemmed | Singular Orbits and Dynamics at Infinity of a Conjugate Lorenz-Like System |
| title_short | Singular Orbits and Dynamics at Infinity of a Conjugate Lorenz-Like System |
| title_sort | singular orbits and dynamics at infinity of a conjugate lorenz like system |
| topic | Hopf bifurcation singularly degenerate heteroclinic cycle homoclinic and heteroclinic orbits Poincare compactification |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/991 |
| work_keys_str_mv | AT fengjiegeng singularorbitsanddynamicsatinfinityofaconjugatelorenzlikesystem AT xianyili singularorbitsanddynamicsatinfinityofaconjugatelorenzlikesystem |