Gunatilake, L.; Shepherd, J. J.; Connell, H. J. Transitions in a non-linear second-order system. (English) Zbl 1342.34055 Int. J. Non-Linear Mech. 34, No. 2, 231-245 (1999). Summary: We investigate the solutions of a second-order system of differential equations corresponding to a pair of coupled non-linear oscillators dependent on a slowly varying parameter. Turning points arise as the parameter evolves through a critical value causing these solutions to exhibit a change in behaviour. We analyse this change by employing asymptotic methods to show that the resulting bifurcation is a type of pitchfork bifurcation. The role of initial conditions in predicting the outcome of the bifurcation is analysed and numerical results are presented. MSC: 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 37G99 Local and nonlocal bifurcation theory for dynamical systems Keywords:Bifurcation; Transition; Turning point; Multiple scales; Matching PDF BibTeX XML Cite \textit{L. Gunatilake} et al., Int. J. Non-Linear Mech. 34, No. 2, 231--245 (1999; Zbl 1342.34055) Full Text: DOI