In this chapter we study a bifurcation characterized by a zero eigenvalue and a pair of nonzero purely imaginary eigenvalues of the linearization transverse to a plane of equilibria. It turns out that instead we can study a one-parameter family of lines in a system depending on one parameter...
ZERO-HOPF BIFURCATION IN INDIRECT FIELD ORIENTED CONTROL OF INDUCTION MOTORS Aracil. Zero-Hopf Bifurcation in Indirect Field Oriented Control of Induction Motors, First IFAC Conference on Analysis and Control of Chaotic Systems: CHAOS... R Reginatto,F Salas,F Gordillo,... - 《Ifac Proceedings ...
Bifurcation Equations Through Multiple-Scales Analysis for a Continuous Model of a Planar Beam It reveals the existence of divergence,Hopf and double-zero bifurcations. The spectral properties of the linear operator and its adjointare studied at the ... A Luongo,AD Egidio - 《Nonlinear Dynamics》...
Sadri, Bifurcation control and universal unfolding for Hopf-zero singu- larities with leading solenoidal terms, ArXiv preprint arXiv:1412.5399 (2015).Gazor, M., Sadri, N.: Bifurcation control and universal unfolding for Hopf-zero singularities with leading solenoidal terms. SIAM J. Appl. Dyn. ...
Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh–Nagumo system Applied Mathematics and Computation, Volume 369, 2020, Article 124893 A. Algaba,…, C. García On the integrability problem for the Hopf-zero singularity an...
In this paper we investigate a particular case of a zero-Hopf bifurcation of a four dimensional analytic differential system. We prove that at most five periodic orbits bifurcate from the zero-Hopf equilibrium using the averaging theory of first order and give a specific example to illustrate thi...
We analyse the zero-Hopf Bifurcation that occur at this point when we persuade a quadratic perturbation of the coefficients, and prove that one, two or three periodic orbits can born when the parameter of the perturbation goes to $0$.
Yuan, "Zero-Hopf bifurcation for an infection-age structured epidemic model with a nonlinear inci- dence rate," Science China Mathematics, vol. 60, no. 8, pp. 1371-1398, 2017.Z. H. Liu and R. Yuan, Zero-Hopf bifurcation for an infection-age structured epidemic model with a nonlinear ...
Hopf bifurcationperiodic solutionIn this paper, we investigate a quadratic chaotic system modeling self-excited and hidden attractors which is described by a system of three nonlinear ordinary differential equations with three real parameters. The primary goal is to establish the existence of two limit...
zero-Hopf bifurcationnormal formperiodic orbitlimit cycleIn recent publications [Llibre, 2014; Llibre & Makhlouf, 2020], time-averaging method was applied to studying periodic orbits bifurcating from zero-Hopf critical points of two Rssler systems. It was shown that the averaging method is ...