Journal ArticleDOI
Limit cycle oscillations and a perturbed harmonic oscillator
Willi-Hans Steeb,A. Kunick +1 more
TLDR
In this article, the behaviour of the dynamical system x = y, y = −x−μ sin y is studied in the context of electrical circuit theory, where the authors focus on the behavior of the system x and y.Abstract:
This note is concerned with the behaviour of the dynamical system x = y, y = −x−μ sin y which is important in electrical circuit theory.read more
Citations
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Chaos in limit cycle systems with external periodic excitations
Willi-Hans Steeb,A. Kunick +1 more
TL;DR: In this paper, the authors investigated limit cycle systems in the plane with an external periodic excitation from the point of view of chaotic behavior, and a singular point analysis was carried out.
Journal ArticleDOI
Solutions to Non-Linear Reaction-Diffusion Equations in Two Space Dimensions
Journal ArticleDOI
Continuous transformation groups and series solution of initial value problems
J.S. Torok,S.H. Advani +1 more
TL;DR: In this article, an efficient method of deriving series solutions of initial value problems is presented, based on the theory of continuous transformation groups, which can be used to solve autonomous and non-autonomous systems of ordinary differential equations.
Journal ArticleDOI
Analysis of the dynamics of new models of nonlinear systems with state variable damping and elastic coefficients
TL;DR: In this article , an analysis of the dynamics of new models of nonlinear systems in which the state damping variables with elastic coefficients, given by functions ccos(px) , csinµ(px), ccosµ (px) and csin µ (σ), are investigated in their autonomous and excited states.
Journal ArticleDOI
Lie series technique, limit cycle systems and dynamical integration
TL;DR: In this paper, the Lie series technique is applied to solve a class of nonlinear differential equations and the dynamical integration technique is used to solve nonlinear systems with chaotic behavior.
References
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Journal ArticleDOI
On the limit cycles of \(\ddot x + \mu \sin \dot x + x = 0\)
Harry Hochstadt,Bruce H. Stephan +1 more
Journal ArticleDOI
Nonlinear autonomous dynamic systems, limit cycles, and one-parameter groups of transformations
TL;DR: The connection between nonlinear autonomous dynamic systems, limit cycles, and one-parameter groups of transformations is described in this article, and an example is given to illustrate the approach.