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Taming chaos arising from dissipative non-autonomous nonlinear systems byapplying additional harmonic excitations is a reliable and widely usedprocedure nowadays. But the suppressory effectiveness of generic non-harmonicperiodic excitations continues to be a significant challenge both to ourtheoretical understanding and in practical applications. Here we show how theeffectiveness of generic suppressory excitations is optimally enhanced when theimpulse transmitted by them (time integral over two consecutive zeros) isjudiciously controlled in a not obvious way. This is demonstratedexperimentally by means of an analog version of a universal model, andconfirmed numerically by simulations of such a damped driven system includingthe presence of noise. Our theoretical analysis shows that the controllingeffect of varying the impulse is due to a correlative variation of the energytransmitted by the suppressory excitation.

Impulse-induced optimum control of chaos in dissipative driven systems