Quasi-periodic solutions can arise in assemblies of nonlinear oscillators as a consequence of Neimark--Sacker (NS) bifurcations. In this chapter, we investigate analytically and numerically the system of two coupled oscillators in two different settings featuring 1:2 and 1:3 internal resonances, respectively. More specifically, in the former case, the locus of NS points is obtained analytically, and its variation with respect to the system parameters is highlighted. In the latter case, on the contrary, the NS boundary curve is investigated numerically. In both cases, the results allow predicting the appearance of quasi-periodic solutions.
Investigation of Quasi-Periodic Solutions in Nonlinear Oscillators Featuring Internal Resonance
Gobat Giorgio;Frangi Attilio;
2022-01-01
Abstract
Quasi-periodic solutions can arise in assemblies of nonlinear oscillators as a consequence of Neimark--Sacker (NS) bifurcations. In this chapter, we investigate analytically and numerically the system of two coupled oscillators in two different settings featuring 1:2 and 1:3 internal resonances, respectively. More specifically, in the former case, the locus of NS points is obtained analytically, and its variation with respect to the system parameters is highlighted. In the latter case, on the contrary, the NS boundary curve is investigated numerically. In both cases, the results allow predicting the appearance of quasi-periodic solutions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
