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Computation of focus values with applications. (English) Zbl 1170.70306

Summary: Computation of focus (or focal) values for nonlinear dynamical systems is not only important in theoretical study, but also useful in applications. In this paper, we compare three typical methods for computing focus values, and give a comparison among these methods. Then, we apply these methods to study two practical problems and Hilbert’s 16th problem. We show that these different methods have the same computational complexity. Finally, we discuss the “minimal singular point value” problem.

MSC:

70-08 Computational methods for problems pertaining to mechanics of particles and systems
70K99 Nonlinear dynamics in mechanics
34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
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