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. © 1988.
Bishop, S. R., Virgin, L. N., & Leung, D. L. M. (1988). On the computation of domains of attraction during the dynamic modelling of oscillating systems. Applied Mathematical Modelling, 12(5), 503–516. https://doi.org/10.1016/0307-904X(88)90088-1