本文利用连续同伦方法讨论非线性映射在有界区域内零点的存在性和零点数目，以及推广若干经典定理。
With homotopy methods, this paper discusses the existence and the number of zeroes of nonlinear mappings on bounded regions and extends some classical theorems.
该模型利用过程神经元网络所具有的对时间变量的非线性映射能力，实现系统的输入、输出之间的连续映射关系。
In this model, the continuous input-output mapping of the system is realized by nonlinear mapping capability to the time variable of process neural networks.
前馈神经网络由于具有理论上逼近任意非线性连续映射的能力，因而非常适合于非线性系统建模及构成自适应控制。
Because the feedforward neural network has an ability of approach to arbitrary nonlinear mapping, it can be used effectively in the modeling and controlling of nonlinear system.
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