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The investigation of the root structure of polynomials with the parametric representation method. (Hungarian) Zbl 0908.34026

In the investigation of dynamical systems a typical problem is the determination of the number of real roots of polynomials. Moreover, the definition of the number of the roots with positive, negative and zero real part is an important question. The authors consider this problem in the case of varying coefficients of polynomials. They investigate the loss of stability. Moreover, a relation between the Routh-Hurwitz criterion and the Hopf bifurcation is established.

MSC:

34C23 Bifurcation theory for ordinary differential equations
37G99 Local and nonlocal bifurcation theory for dynamical systems
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