Geodesic
Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers
Kybernetika, Tome 44 (2008) no. 1, pp. 35-42.

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A four-dimensional hyperchaotic Lü system with multiple time-delay controllers is considered in this paper. Based on the theory of Hopf bifurcation in delay system, we obtain a simple relationship between the parameters when the system has a periodic solution. Numerical simulations show that the assumption is a rational condition, choosing parameter in the determined region can control hyperchaotic Lü system well, the chaotic state is transformed to the periodic orbit. Finally, we consider the differences between the analysis of the hyperchaotic Lorenz system, hyperchaotic Chen system and hyperchaotic Lü system.
Classification : 34K18, 37D45, 37N35, 93C15
Keywords: Hopf bifurcation; periodic solution; multiple delays and parameters; hyperchaotic Lü system; hyperchaotic Chen system; hyperchaotic Lorenz system 
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     author = {Zhang, Lan and Zhang, Chengjian},
     title = {Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers},
     journal = {Kybernetika},
     pages = {35--42},
     publisher = {mathdoc},
     volume = {44},
     number = {1},
     year = {2008},
     mrnumber = {2405053},
     zbl = {1145.93361},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2008__44_1_a2/}
}
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Zhang, Lan; Zhang, Chengjian. Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers. Kybernetika, Tome 44 (2008) no. 1, pp. 35-42. http://geodesic.mathdoc.fr/item/KYB_2008__44_1_a2/