分岔系统中非零解的近似表示
On The Approximative Expression of the Nonzero Solution in A Bifurcation System
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摘要: 作者曾研究过带有一个参数的非线性矢量常微分方程所描述的分岔系统,得到了这类系 统存在非零平衡解的必要条件和充分条件,获得了非零平衡解的精确个数.本文研究非零平 衡解的近似表示问题,得出其近似表示式,所得结果有助于了解平衡解的实际位置及其对参 数的依赖状况,有助于研究分岔系统轨线的特性.Abstract: Author has studied a bifurcation system which is described by a nonlinear vectorial ordinary differential equation with a parameter. The necessary condition and sufficient conditions for the system to have a nonzero equilibrium solution, and the exact: number of nonzero equilibrium solutions were obtained. In this paper, the problem on the approximation of a nonzero equilibrium solution is discussed. The results is useful to understand the real position of nonzero equilibrium states and to study the behaviour of the trajectories of a bifurcation system.
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