The zero-Hopf bifurcations of a four-dimensional hyperchaotic system
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tian, Yuzhou (Sun Yat-sen University. School of Mathematics (Zhuhai))

Date:	2021
Abstract:	We consider the four-dimensional hyperchaotic system ẋ=a(y-x), y˙=bx+u-y-xz, ż=xy-cz, and u˙=-du-jx+exz, where a, b, c, d, j, and e are real parameters. This system extends the famous Lorenz system to four dimensions and was introduced in Zhou et al. , Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, 1750021 (2017). We characterize the values of the parameters for which their equilibrium points are zero-Hopf points. Using the averaging theory, we obtain sufficient conditions for the existence of periodic orbits bifurcating from these zero-Hopf equilibria and give some examples to illustrate the conclusions. Moreover, the stability conditions of these periodic orbits are given using the Routh-Hurwitz criterion.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Published in:	Journal of Mathematical Physics, Vol. 62, Issue 5 (May 2021) , art. 052703, ISSN 1089-7658

DOI: 10.1063/5.0023155

10 p, 4.2 MB

Postprint 12 p, 755.8 KB

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