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Generalized form of Hurwitz-Routh criterion and Hopf bifurcation of higher order. (English) Zbl 1006.34041
Summary: The well-known Hurwitz-Routh criterion is generalized to critical cases. The problem of Hopf bifurcation of higher order for zeros of semistable polynomials is also discussed.

MSC:
34D20 Stability of solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
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References:
[1] Brauer, F.; Nohel, J.A., ()
[2] Liu, W., Criterion of Hopf bifurcation without using eigenvalues, J. math. anal. appl., 182, 250-256, (1994) · Zbl 0794.34033
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