New analytical technique for predicting homoclinic bifurcations in autonomous dynamical systems
type: Item
instance of: scholarly article
title: New analytical technique for predicting homoclinic bifurcations in autonomous dynamical systems
zbMATH Open document ID: 0934.37013
DOI: 10.1016/S0093-6413(98)00006-8
published in: Mechanics Research Communications
publication date: 2000-04-13T00:00:00Z
review text: The author considers planar differential equations \(\dot{x} = y\), \(\dot{y} = -\lambda x + \epsilon f(x,y,\mu)\), where \(\epsilon\) is a small parameter and \(\mu\) are other parameters. Approximating solutions by averaging, equations for homoclinic solutions are derived by looking for collisions of limit cycles with equilibria of saddle type. Not much justification is given, but a number of examples are discussed where the results are compared with Melnikov's method to locate homoclinic solutions.
reviewed by: Ale Jan Homburg
Mathematics Subject Classification ID: 37C29
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 1216529
zbMATH Keywords: planar differential equations
zbMATH Keywords: averaging
zbMATH Keywords: homoclinic solutions
zbMATH Keywords: limit cycles
zbMATH Keywords: Melnikov's method
author: Mohamed Belhaq
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1216529