TY - JOUR
T1 - Converting a general 3-d autonomous quadratic system to an extended lorenz-type system
AU - Hua, Cuncai
AU - Chen, Guanrong
AU - Li, Qunhong
AU - Ge, Juhong
PY - 2011/9
Y1 - 2011/9
N2 - A problem of reducing a general three-dimensional (3-D) autonomous quadratic system to a Lorenz-type system is studied. Firstly, under some necessary conditions for preserving the basic qualitative properties of the Lorenz system, the general 3-D autonomous quadratic system is converted to an extended Lorenz-type system (ELTS) which contains a large class of existing chaotic dynamical systems. Secondly, some different canonical forms of the ELTS are obtained with the aid of various nonsingular linear transformations and normalization techniques. Thirdly, the conjugate systems of the ELTS are defined and discussed. Finally, a sufficient condition for the nonexistence of chaos in such ELTS is derived.
AB - A problem of reducing a general three-dimensional (3-D) autonomous quadratic system to a Lorenz-type system is studied. Firstly, under some necessary conditions for preserving the basic qualitative properties of the Lorenz system, the general 3-D autonomous quadratic system is converted to an extended Lorenz-type system (ELTS) which contains a large class of existing chaotic dynamical systems. Secondly, some different canonical forms of the ELTS are obtained with the aid of various nonsingular linear transformations and normalization techniques. Thirdly, the conjugate systems of the ELTS are defined and discussed. Finally, a sufficient condition for the nonexistence of chaos in such ELTS is derived.
KW - Bifurcation analysis
KW - Lorenz-type system
KW - Three-dimensional autonomous quadratic system
UR - http://www.scopus.com/inward/record.url?scp=79960349300&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-79960349300&origin=recordpage
U2 - 10.3934/dcdsb.2011.16.475
DO - 10.3934/dcdsb.2011.16.475
M3 - RGC 21 - Publication in refereed journal
SN - 1531-3492
VL - 16
SP - 475
EP - 488
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
IS - 2
ER -