Publication Date:
2016-01-06
Description:
We carry out a systematic qualitative analysis of the two quadratic schemes of generalized oscillators recently proposed by Quesne [J. Math. Phys. 56 , 012903 (2015)]. By performing a local analysis of the governing potentials, we demonstrate that while the first potential admits a pair of equilibrium points one of which is typically a center for both signs of the coupling strength λ , the other points to a centre for λ 〈 0 but a saddle λ 〉 0. On the other hand, the second potential reveals only a center for both the signs of λ from a linear stability analysis. We carry out our study by extending Quesne’s scheme to include the effects of a linear dissipative term. An important outcome is that we run into a remarkable transition to chaos in the presence of a periodic force term f cos ωt .
Print ISSN:
0022-2488
Electronic ISSN:
1089-7658
Topics:
Mathematics
,
Physics
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