Automatic analysis of one-parameter planar ordinary differential equations by intelligent numeric simulation

DOI10.1016/0004-3702(91)90079-YzbMath0714.65068OpenAlexW2041163775MaRDI QIDQ751202

Elisha P. Sacks

Publication date: 1991

Published in: Artificial Intelligence (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0004-3702(91)90079-y

zbMATH Keywords

fixed pointslimit cyclesbifurcationsphase diagramsautonomous systemsprogram POINCAREsaddle manifoldsuniform asymptotic behaviour

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence (68T35) Numerical methods for initial value problems involving ordinary differential equations (65L05) Dynamical systems and ergodic theory (37-XX) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

Related Items (10)

Extracting and representing qualitative behaviors of complex systems in phase space ⋮ Artificial intelligence in economics ⋮ Computational dynamics: Modeling and visualizing trajectory flows in phase space. ⋮ Qualitative and quantitative simulation: bridging the gap ⋮ Grammatical description of behaviors of ordinary differential equations in two-dimensional phase space ⋮ AUTONOMOUS EXPLORATION AND CONTROL OF CHAOTIC SYSTEMS ⋮ Automated analysis of qualitative behaviors of piecewise linear ordinary differential equations ⋮ Reasoning about model accuracy ⋮ Continuous interpolation logic and qualitative modeling of flows ⋮ Using modeling knowledge to guide design space search

Uses Software

• ODESSA
• AUTO
• AUTO-86

Cites Work

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• Perturbation methods, bifurcation theory and computer algebra
• A dynamic systems perspective on qualitative simulation
• The simultaneous solution and sensitivity analysis of systems described by ordinary differential equations

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