On the computation of domains of attraction during the dynamic modelling of oscillating systems

• Published in: Applied mathematical modelling Vol. 12; no. 5; pp. 503 - 516
• Main Authors: Bishop, Steve R, Virgin, Lawrence N, Leung, Dennis L.M
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.10.1988; Elsevier Science
• Subjects: catchment regions; domains of attraction; Exact sciences and technology; fractal basin boundaries; Fundamental areas of phenomenology (including applications); nonlinear dynamics; offshore mechanics; Physics; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics; subharmonic resonances; catchment regions; subharmonic resonances; domains of attraction; nonlinear dynamics; fractal basin boundaries; offshore mechanics; Dynamic response; Offshore structure; Non linear system; Oscillator; Modeling
• ISSN: 0307-904X
• DOI: 10.1016/0307-904X(88)90088-1

A particular feature of nonlinear differential equations is that they may have competing steady-state solutions. This paper describes some multiple dynamic responses typically found when modelling nonlinear systems with particular reference to the catchment regions which illustrate sensitivity to initial conditions. The form of dynamic behavior persisting after the decay of transient motion due to damping depends on the starting conditions in terms of initial displacement and velocity of the system. Methods of obtaining domains of attraction to particular stable solutions are described with reference to simple equations incorporating nonlinear resonance phenomena together with examples of coexisting subharmonic oscillations in offshore mechanics.