Stability on finite time interval and time-dependent bifurcation analysis of Duffing's equations
type: Item
instance of: scholarly article
title: Stability on finite time interval and time-dependent bifurcation analysis of Duffing's equations
zbMATH Open document ID: 0947.34025
DOI: 10.1016/S1007-5704(99)90039-4
author: Cuncai Hua
author: Q.-S. Lu
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2000-10-25T00:00:00Z
review text: Let \(f: \mathbb{R}^n \times \mathbb{R} \rightarrow \mathbb{R}^n\) be continuously differentiable satisfying \(f(0,0)=0,\) let \(f_x (0,0)\) be singular. The authors are interested in studying the dynamic bifurcation problem \(dx/dt = f(x,\lambda)\) with \(\lambda = \lambda (\varepsilon t)\) where \(\varepsilon\) is a small parameter. To this purpose the concept of the stability on a finite time interval is introduced and some theorems related to that topic are formulated. They apply their results to the time-dependent Duffing equation \( \ddot{x} + k \dot{x} = \lambda (\varepsilon t)x-x^3\) to determine the delayed bifurcation behavior.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34K18
zbMATH DE Number: 1420501
zbMATH Keywords: dynamic bifurcation
zbMATH Keywords: Duffing's equation
zbMATH Keywords: stability on finite time interval
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
cites work: Slowly Varying Jump and Transition Phenomena Associated with Algebraic Bifurcation Problems
cites work: Parametric studies of the dynamic evolution through a fold
cites work: Slow Passage Through a Pitchfork Bifurcation
cites work: Sudden change in a second-order nonlinear system with a slowly varying parameter
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full work available at URL: s1007-5704(99)90039-4
OpenAlex ID: W2037787679
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description: scientific article; zbMATH DE number 1420501