Quadratic Polynomial Systems with Degenerate Critical Point
Keywords:
Quadratic Polynomial Systems, Critical No hyperbolic, Degenerate Critical Point, Qualitative Analysis, phase portraits of polynomial systems.Abstract
This article presents a qualitative analysis is presented quadratic systems that They have at most two critical points where one is a point degenerate critical to this first identify and classify quadratic systems with a degenerate critical point and thus facilitate their study and then phase portraits obtained from analysis are plotted
These qualitative sistemas. For this study the quadratic systems differential quations was necessary to use some results important on the theory of textit systems not Linear , therefore they included some definitions and theorems that were vital for the study, as they determine the next steps for the qualitative analysis of any nonlinear system.
References
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Guckeinheimer, J., y Holmes, P. 1983, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields ( New York: Springer Verlag).
Hagedorn, P. 1982, Nonlinear Oscillations ( Oxford: Clarendon Press).
Perko,L. 2001, Differential Equations and Dynamical Systems (New York: Springer Verlag).
Dumortier, F., Llibre, J., y Artés, J. 2006, Qualitative Theory of PLanar Differential Systems (Berlin: Springer Verlag).
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