Dynamics of a New Hyperchaotic System with Only One Equilibrium Point | Zendy

Xiang Li | Zendy; Ranchao Wu | Zendy

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Dynamics of a New Hyperchaotic System with Only One Equilibrium Point

Author(s) -

Xiang Li,

Ranchao Wu

Publication year - 2013

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2013/935384

Subject(s) - mathematics , attractor , hopf bifurcation , bifurcation , equilibrium point , constant (computer programming) , pitchfork bifurcation , lorenz system , control theory (sociology) , biological applications of bifurcation theory , saddle node bifurcation , mathematical analysis , nonlinear system , control (management) , computer science , physics , differential equation , quantum mechanics , artificial intelligence , programming language

A new 4D hyperchaotic system is constructed based on the Lorenz system. The compound structure and forming mechanism of the new hyperchaotic attractor are studied via a controlled system with constant controllers. Furthermore, it is found that the Hopf bifurcation occurs in this hyperchaotic system when the bifurcation parameter exceeds a critical value. The direction of the Hopf bifurcation as well as the stability of bifurcating periodic solutions is presented in detail by virtue of the normal form theory. Numerical simulations are given to illustrate and verify the results.

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