Automatic analysis of one-parameter planar ordinary differential equations by intelligent numeric simulation
type: Item
instance of: scholarly article
title: Automatic analysis of one-parameter planar ordinary differential equations by intelligent numeric simulation
zbMATH Open document ID: 0714.65068
DOI: 10.1016/0004-3702(91)90079-Y
author: Elisha Sacks
published in: Artificial Intelligence
publication date: 1991-01-01T00:00:00Z
review text: A program called Poincare is given, which analyzes one-parameter autonomous systems of two differential equations. The program partitions the parameter interval into open subintervals of equivalent behaviour. It detects local and global generic one-parameter bifurcations and constructs the phase diagrams by identifying fixed points, saddle manifolds, limit cycles and partitioning the remaining trajectories into open regions of uniform asymptotic behaviour.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65C20
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 68T35
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34-04
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 4176373
zbMATH Keywords: program POINCARE
zbMATH Keywords: autonomous systems
zbMATH Keywords: bifurcations
zbMATH Keywords: phase diagrams
zbMATH Keywords: fixed points
zbMATH Keywords: saddle manifolds
zbMATH Keywords: limit cycles
zbMATH Keywords: uniform asymptotic behaviour
reviewed by: Miroslav Bartušek
describes a project that uses: AUTO
describes a project that uses: AUTO-86
describes a project that uses: ODESSA
MaRDI profile type: Publication
cites work: Q4067388
cites work: Q3708330
cites work: The simultaneous solution and sensitivity analysis of systems described by ordinary differential equations
cites work: Q4040287
cites work: Q3992847
cites work: Perturbation methods, bifurcation theory and computer algebra
cites work: A dynamic systems perspective on qualitative simulation
cites work: Q3736576
full work available at URL: 0004-3702(91)90079-y
OpenAlex ID: W2041163775
description: scientific article; zbMATH DE number 4176373