This paper presents an affirmative answer to the heretofore unresolved question as to whether an autonomous nonlinear system can always be synthesized to possess a finite number of prescribed singular points, as well as a prescribed set of eigenvalues associated with each singular point. The answer is given in the form of a new canonic nth-order nonlinear system containing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(3n-2)</tex> single-valued functions. In the case <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n=2</tex> the canonic system is shown to possess many nice general properties which are useful for determining aspects of the system's global qualitative behavior, such as global stability.
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