Extended Jury criterion. (English) Zbl 1189.37059

Summary: Algebraic criteria are established to determine whether or not a real coefficient polynomial has one or two pairs of conjugate complex roots whose moduli are equal to 1 and the other roots have moduli less than 1 directly from its coefficients. The form and the function of the criteria are similar to those of the Jury criterion which can be used to determine whether or not all the moduli of the roots of a real coefficient polynomial are less than 1.


37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
12Y05 Computational aspects of field theory and polynomials (MSC2010)
Full Text: DOI


[1] Jury I. Inners and Stability of Dynamic Systems. London: John Wiley, 1974 · Zbl 0307.93025
[2] Liang S, Zhang J. A complete discrimination system for polynomials with complex coefficients and its automatic generation. Sci China Ser E, 1999, 42: 113–128 · Zbl 0949.12002
[3] Liao X. On asymptotic behavior of solutions to several classes of discrete dynamical systems. Sci China Ser A, 2002, 45: 432–442 · Zbl 1107.93029
[4] Nian X. New criteria on the stability of interval discrete dynamic systems. Control Theory and Applications, 1999, 16: 558–561 · Zbl 1002.93045
[5] Wu Z, Liu W. Criterion of high-codimensional bifurcations with several pairs of purely imaginary eigenvalues. Linear Algebra Appl, 1997, 267: 53–63 · Zbl 0889.34035
[6] Zhang J, Yang L, Hou X. A criterion for dependency of algebraic equations with applications to automated theorem proving. Sci China Ser A, 1994, 37: 547–554 · Zbl 0820.68108
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.