Li, Enying; Li, Guangyao; Wen, Guilin; Wang, Hu Hopf bifurcation of the third-order Hénon system based on an explicit criterion. (English) Zbl 1158.93364 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 9, 3227-3235 (2009). Summary: Hopf bifurcation of the third-order Hénon system is studied via a simple explicit criterion, which is derived from the Schur-Cohn Criterion. Moreover, stability of Hopf bifurcation is also investigated by using the normal form method and center manifold theory for the discrete time system developed by Kuznetsov. Test results containing simulations and circuit measurement are shown to demonstrate that the criterion is correct and feasible. Cited in 1 Document MSC: 93C55 Discrete-time control/observation systems 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior Keywords:Hopf bifurcation; explicit criterion; stability; Hénon map; circuit implementation; simulation; limit cycle PDFBibTeX XMLCite \textit{E. Li} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 9, 3227--3235 (2009; Zbl 1158.93364) Full Text: DOI References: [1] Porter, B., Stability Criteria for Linear Dynamical Systems (1967), Oliver & Boyd: Oliver & Boyd London [2] Yu, P., Closed-form conditions of bifurcation points for general differential equations, International Journal of Bifurcation and Chaos, 15, 4, 1467-1483 (2005) · Zbl 1090.34034 [3] Kuo, C., Analysis and Synthesis of Sampled-Data Control Systems (1963), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ [4] Lasalle, J. P., The Stability and Control of Discrete Processes (1986), Springer-Verlag: Springer-Verlag Berlin · Zbl 0606.93001 [5] Wen, Guilin, Criterion to identify Hopf bifurcations in maps of arbitrary dimension, Physical Reviw E, 72, 026201 (2005) [6] Wen, Guilin; Xu, Daolin, Control algorithm for creation of Hopf bifurcations in continuous-time systems of arbitrary dimension, Physics Letters A, 337, 93-100 (2005) · Zbl 1135.37318 [7] Kuznetsov, Y. A., Elements of Applied Bifurcation Theory (1998), Springer-Verlag: Springer-Verlag New York · Zbl 0914.58025 [8] Baier, G.; Klein, M., Maximum hyperchaos in generalized Hénon circuit, Physics Letters A, 151, 67, 281-284 (1990) [9] D.A. Miller, G. Grassi, A discrete generalized hyperchaotic Hénon map circuit, in Proc.of the 44th IEEE Midwest Symposium on Circuits and Systems, vo. 1, 2001, p. 328; D.A. Miller, G. Grassi, A discrete generalized hyperchaotic Hénon map circuit, in Proc.of the 44th IEEE Midwest Symposium on Circuits and Systems, vo. 1, 2001, p. 328 [10] Grassi, G.; Miller, D. A., Theory and experimental realization of observer-based discrete-time hyperchaos synchronization, IEEE Transactions on CAS-I, 49, 3, 373-378 (2002) [11] Grassi, G.; Miller, D. A., Projective synchronization via a linear observer: Application to time-delay, continuous-time, and discrete-time systems, International Journal of Bifurcation and Chaos, 17, 4, 1337-1342 (2007) · Zbl 1139.93348 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.