Bifurcation analysis and dynamics of a Lorenz –type dynamical system
./files/site1/files/0Abstract1.pdfIn this paper we consider a continues Lorenz – type dynamical system. Dynamical behaviors of this system such as computing equilibrium points, different bifurcation curves and computation of normal form coefficient of each bifurcation point analytically and numerica...
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| Format: | Article |
| Language: | fas |
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Kharazmi University
2017-12-01
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| Series: | پژوهشهای ریاضی |
| Subjects: | |
| Online Access: | http://mmr.khu.ac.ir/article-1-2692-en.html |
| _version_ | 1797871737489063936 |
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| author | Behnaz Rahmani Reza Khoshsiar Mohammad ShfieDehaghin Neda Ahanjideh |
| author_facet | Behnaz Rahmani Reza Khoshsiar Mohammad ShfieDehaghin Neda Ahanjideh |
| author_sort | Behnaz Rahmani |
| collection | DOAJ |
| description | ./files/site1/files/0Abstract1.pdfIn this paper we consider a continues Lorenz – type dynamical system. Dynamical behaviors of this system such as computing equilibrium points, different bifurcation curves and computation of normal form coefficient of each bifurcation point analytically and numerically. In particular we derived sufficient conditions for existence of Hopf and Pitchfork bifurcations and determined criticality of these bifurcations. By means of numerical simulations, we show that the system may have chaotic behavior under some conditions. By employing numerical continuation method, we first compute bifurcation curves and then compute all codimension 1 and 2 bifurcation along these curves with determined of the corresponding normal form coefficient. |
| first_indexed | 2024-04-10T00:47:23Z |
| format | Article |
| id | doaj.art-89d209477ad54202bb4aab44b458613b |
| institution | Directory Open Access Journal |
| issn | 2588-2546 2588-2554 |
| language | fas |
| last_indexed | 2024-04-10T00:47:23Z |
| publishDate | 2017-12-01 |
| publisher | Kharazmi University |
| record_format | Article |
| series | پژوهشهای ریاضی |
| spelling | doaj.art-89d209477ad54202bb4aab44b458613b2023-03-13T19:18:57ZfasKharazmi Universityپژوهشهای ریاضی2588-25462588-25542017-12-013385104Bifurcation analysis and dynamics of a Lorenz –type dynamical systemBehnaz Rahmani0Reza Khoshsiar1Mohammad ShfieDehaghin2Neda Ahanjideh3 ./files/site1/files/0Abstract1.pdfIn this paper we consider a continues Lorenz – type dynamical system. Dynamical behaviors of this system such as computing equilibrium points, different bifurcation curves and computation of normal form coefficient of each bifurcation point analytically and numerically. In particular we derived sufficient conditions for existence of Hopf and Pitchfork bifurcations and determined criticality of these bifurcations. By means of numerical simulations, we show that the system may have chaotic behavior under some conditions. By employing numerical continuation method, we first compute bifurcation curves and then compute all codimension 1 and 2 bifurcation along these curves with determined of the corresponding normal form coefficient.http://mmr.khu.ac.ir/article-1-2692-en.htmlsystemhopf bifurcationpitchfork bifurcationnormal formfirst lyapunove coefficient |
| spellingShingle | Behnaz Rahmani Reza Khoshsiar Mohammad ShfieDehaghin Neda Ahanjideh Bifurcation analysis and dynamics of a Lorenz –type dynamical system پژوهشهای ریاضی system hopf bifurcation pitchfork bifurcation normal form first lyapunove coefficient |
| title | Bifurcation analysis and dynamics of a Lorenz –type dynamical system |
| title_full | Bifurcation analysis and dynamics of a Lorenz –type dynamical system |
| title_fullStr | Bifurcation analysis and dynamics of a Lorenz –type dynamical system |
| title_full_unstemmed | Bifurcation analysis and dynamics of a Lorenz –type dynamical system |
| title_short | Bifurcation analysis and dynamics of a Lorenz –type dynamical system |
| title_sort | bifurcation analysis and dynamics of a lorenz type dynamical system |
| topic | system hopf bifurcation pitchfork bifurcation normal form first lyapunove coefficient |
| url | http://mmr.khu.ac.ir/article-1-2692-en.html |
| work_keys_str_mv | AT behnazrahmani bifurcationanalysisanddynamicsofalorenztypedynamicalsystem AT rezakhoshsiar bifurcationanalysisanddynamicsofalorenztypedynamicalsystem AT mohammadshfiedehaghin bifurcationanalysisanddynamicsofalorenztypedynamicalsystem AT nedaahanjideh bifurcationanalysisanddynamicsofalorenztypedynamicalsystem |