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A one‐dimensional model of dynamics for a class of third‐order systems
Author(s) -
Ogorzalek Maciej J.
Publication year - 1990
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490180606
Subject(s) - class (philosophy) , spiral (railway) , third order , bifurcation , mathematics , differential equation , order (exchange) , system dynamics , dynamics (music) , trajectory , computer science , mathematical analysis , nonlinear system , artificial intelligence , physics , philosophy , theology , finance , quantum mechanics , astronomy , acoustics , economics
For a class of third‐order non‐linear systems whose dynamics is governed by a differential equation of the formwe propose a one‐dimensional model reflecting the dynamic properties of the original system. Construction of this model map has been based on analysis of the trajectory behaviour in the original third‐order system. Properties of the model map have been investigated. Experiments have proved that the proposed one‐dimensional map, termed a deformed spiral map, reproduces the qualitative behaviour (e.g. bifurcation sequences) of the original system with very good accuracy.