Effect of delayed feedback on the dynamics of a scalar map via a frequency-domain approach |
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| Authors: | Gentile Franco S Bel Andrea L Belén D'Amico M Moiola Jorge L |
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| Institution: | Instituto de Investigaciones en Ingenieri?a Eli?ctrica Alfredo Desages (UNS-CONICET), Departamento de Ingenieri?a Ele?ctrica y de Computadoras, Universidad Nacional del Sur, Av. Alem 1253, B8000CPB Bahi?a Blanca, Argentina. franco.gentile@uns.edu.ar |
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| Abstract: | The effect of delayed feedback on the dynamics of a scalar map is studied by using a frequency-domain approach. Explicit conditions for the occurrence of period-doubling and Neimark-Sacker bifurcations in the controlled map are found analytically. The appearance of a 1:2 resonance for certain values of the delay is also formalized, revealing that this phenomenon is independent of the system parameters. A detailed study of the well-known logistic map under delayed feedback is included for illustration. |
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