zbMATH — the first resource for mathematics

Transitions in a non-linear second-order system. (English) Zbl 1342.34055
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.
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
37G99 Local and nonlocal bifurcation theory for dynamical systems
Full Text: DOI