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Experimental mastering of nonlinear dynamics in circuits by sporadic pulses

Journal: Chaos, Solitions and Fractals
Year: 2008   Volume: 36
Initial page: 635   Last page: 645
Status: Published
PDF file: 2008_gutierrez_CSF.pdf
Ruiz, P., , Guémez, J.

We present some experimental evidence of mastering chaos (control and anticontrol) in nonlinear circuits using a simple impulsive method which does not require any knowledge about the system’s dynamics. The method works by introducing instantaneous pulses in some system variables—in this paper the pulses are applied to a capacitor voltage— and, hence, is an additional plug-in that does not modify the system itself. When varying the mastering parameters (amplitude and frequency of pulses) we obtain a bifurcation structure similar to the one obtained when varying some system’s parameters. Therefore, this device allows us investigating the dynamics of a given circuit providing us with a versatile component for performing both control or anticontrol of chaos. In particular, we show how a double-scroll chaotic system is stabilized in period three, single-scroll, period-4, period-2, period-1, fixed point, following an inverse bifurcation route as a function of the pulses amplitude (chaos control). It is also shown how a periodic Chua’s circuit is driven to chaotic behavior (chaos anticontrol).