A Monge-Ampère type fully nonlinear equation on Hermitian manifolds
Bo Guan Qun Li
We study a fully nonlinear equation of complex Monge-Ampère type on Hermitian manifolds. We establish the a priori estimates for solutions of the equation up to the second order derivatives with the help of a subsolution.
keywords: a priori estimates. fully nonlinear equations Hermitian manifolds Complex Monge-Ampère equations
Converting a general 3-D autonomous quadratic system to an extended Lorenz-type system
Cuncai Hua Guanrong Chen Qunhong Li Juhong Ge
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.
keywords: Three-dimensional autonomous quadratic system bifurcation analysis. Lorenz-type system

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