Dynamical behaviors and synchronization in the fractional order hyperchaotic Chen system. (English) Zbl 1234.34036

Hegazi, A. S.; Matouk, A. E.

Appl. Math. Lett. 24, No. 11, 1938-1944 (2011).

Summary: Some dynamical behaviors are studied in the fractional order hyperchaotic Chen system which shows hyperchaos with order less than 4. The analytical conditions for achieving synchronization in this system via linear control are investigated theoretically by using the Laplace transform theory. Routh-Hurwitz conditions and numerical simulations are used to show the agreement between the theoretical and numerical results. To the best of our knowledge this is the first example of a hyperchaotic system synchronizable just in the fractional order case, using a specific choice of controllers.

MSC:

34D06	Synchronization of solutions to ordinary differential equations
26A33	Fractional derivatives and integrals
34C28	Complex behavior and chaotic systems of ordinary differential equations
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35	Dynamical systems in control

Keywords:

fractional order; hyperchaotic Chen system; Routh-Hurwitz conditions; hyperchaos; synchronization

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