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A hyperchaotic system from the Rabinovich system. (English) Zbl 1191.37023
A four-dimensional system as an extension of three dimensional Rabinovich system is studied. It is proved that the presented system is a hyperchaotic system for a special value of parameters. In fact two positive Lyapunov exponents for the system have detected. The authors also proved that the four-dimensional system has z-axis symmetry and its attractor has double-lobe structure such as the Robinovich system. The existence of a Hopf bifurcation at the origin for a special value of the controller parameter has proved. Lyapunov exponents and bifurcation have investigated numerically. The suggested system is a new system for understanding the hyperchaotic behavior.

##### MSC:
 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
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