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Qualitative analysis of certain generalized classes of quadratic oscillator systems
- Source :
- J.Math.Phys.57,022701(2016)
- Publication Year :
- 2015
-
Abstract
- We carry out a systematic qualitative analysis of the two quadratic schemes of generalized oscillators recently proposed by C. Quesne [J.Math.Phys.\textbf{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 $\lambda$, the other points to a centre for $\lambda < 0$ but a saddle $\lambda > 0$. On the other hand, the second potential reveals only a center for both the signs of $\lambda$ 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 $f\cos \omega t$.<br />Comment: 12 pages, 6 figures, Accepted for Publication in J.Math.Phys
- Subjects :
- Mathematical Physics
Nonlinear Sciences - Chaotic Dynamics
Subjects
Details
- Database :
- arXiv
- Journal :
- J.Math.Phys.57,022701(2016)
- Publication Type :
- Report
- Accession number :
- edsarx.1511.02054
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1063/1.4939486