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Title: Qualitative analysis of certain generalized classes of quadratic oscillator systems

Abstract

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 fcosωt.

Authors:
; ; ;  [1]
  1. Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009 (India)
Publication Date:
OSTI Identifier:
22479634
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 2; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; COUPLING; EQUILIBRIUM; OSCILLATORS; PERIODICITY; POTENTIALS; STABILITY

Citation Formats

Bagchi, Bijan, E-mail: bbagchi123@gmail.com, Ghosh, Samiran, E-mail: sran-g@yahoo.com, Pal, Barnali, E-mail: barrna.roo@gmail.com, and Poria, Swarup, E-mail: swarupporia@gmail.com. Qualitative analysis of certain generalized classes of quadratic oscillator systems. United States: N. p., 2016. Web. doi:10.1063/1.4939486.
Bagchi, Bijan, E-mail: bbagchi123@gmail.com, Ghosh, Samiran, E-mail: sran-g@yahoo.com, Pal, Barnali, E-mail: barrna.roo@gmail.com, & Poria, Swarup, E-mail: swarupporia@gmail.com. Qualitative analysis of certain generalized classes of quadratic oscillator systems. United States. doi:10.1063/1.4939486.
Bagchi, Bijan, E-mail: bbagchi123@gmail.com, Ghosh, Samiran, E-mail: sran-g@yahoo.com, Pal, Barnali, E-mail: barrna.roo@gmail.com, and Poria, Swarup, E-mail: swarupporia@gmail.com. 2016. "Qualitative analysis of certain generalized classes of quadratic oscillator systems". United States. doi:10.1063/1.4939486.
@article{osti_22479634,
title = {Qualitative analysis of certain generalized classes of quadratic oscillator systems},
author = {Bagchi, Bijan, E-mail: bbagchi123@gmail.com and Ghosh, Samiran, E-mail: sran-g@yahoo.com and Pal, Barnali, E-mail: barrna.roo@gmail.com and Poria, Swarup, E-mail: swarupporia@gmail.com},
abstractNote = {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 fcosωt.},
doi = {10.1063/1.4939486},
journal = {Journal of Mathematical Physics},
number = 2,
volume = 57,
place = {United States},
year = 2016,
month = 2
}