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Pàgina inicial > Articles > Articles publicats > The zero-Hopf bifurcations of a four-dimensional hyperchaotic system |
Data: | 2021 |
Resum: | 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. |
Ajuts: | Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió publicada |
Publicat a: | Journal of Mathematical Physics, Vol. 62, Issue 5 (May 2021) , art. 052703, ISSN 1089-7658 |
10 p, 4.2 MB |
Postprint 12 p, 755.8 KB |