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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.
MSC:
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
37G99 Local and nonlocal bifurcation theory for dynamical systems
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