BIFURCATION ANALYSIS AND DYNAMICS OF A LORENZ –TYPE DYNAMICAL SYSTEM

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RAHMANI BEHNAZ; Khoshsiar Reza; SHFIEDEHAGHIN MOHAMMAD; AHANJIDEH NEDA

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Journal: MATHEMATICAL RESEARCHES Year:2017 | Volume:3 | Issue:2 Page(s): 85-104

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Title

BIFURCATION ANALYSIS AND DYNAMICS OF A LORENZ –TYPE DYNAMICAL SYSTEM

Author(s)

RAHMANI BEHNAZ | Khoshsiar Reza | SHFIEDEHAGHIN MOHAMMAD | AHANJIDEH NEDA | Issue Writer Certificate

Keywords

SYSTEMQ1

HOPF BIFURCATIONQ1

PITCHFORK BIFURCATIONQ1

NORMAL FORMQ1

FIRST LYAPUNOVE COEFFICIENTQ1

Abstract

In 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.

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APA: Copy

RAHMANI, BEHNAZ, Khoshsiar, Reza, SHFIEDEHAGHIN, MOHAMMAD, & AHANJIDEH, NEDA. (2017). BIFURCATION ANALYSIS AND DYNAMICS OF A LORENZ –TYPE DYNAMICAL SYSTEM. MATHEMATICAL RESEARCHES, 3(2 ), 85-104. SID. https://sid.ir/paper/260781/en

Vancouver: Copy

RAHMANI BEHNAZ, Khoshsiar Reza, SHFIEDEHAGHIN MOHAMMAD, AHANJIDEH NEDA. BIFURCATION ANALYSIS AND DYNAMICS OF A LORENZ –TYPE DYNAMICAL SYSTEM. MATHEMATICAL RESEARCHES[Internet]. 2017;3(2 ):85-104. Available from: https://sid.ir/paper/260781/en

IEEE: Copy

BEHNAZ RAHMANI, Reza Khoshsiar, MOHAMMAD SHFIEDEHAGHIN, and NEDA AHANJIDEH, “BIFURCATION ANALYSIS AND DYNAMICS OF A LORENZ –TYPE DYNAMICAL SYSTEM,” MATHEMATICAL RESEARCHES, vol. 3, no. 2 , pp. 85–104, 2017, [Online]. Available: https://sid.ir/paper/260781/en

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