The bifurcation structure of a dual-frequency driven, second order nonlinear oscillator (Keller–Miksis equation) is investigated by exploiting the high computational resources of professional GPUs. The numerical scheme of the applied initial value problem solver was the explicit, adaptive Runge–Kutta–Cash–Karp method with embedded error estimation using solutions of order 4 and 5. The four dimensional parameter space (amplitudes and frequencies of the driving) is explored by means of several high resolution bi-parametric plots with the amplitudes as control parameters at fixed frequencies. The resolution of the control parameter plane is 500 × 500 with 10 initial conditions at each parameter pair (altogether 2.5 million initial value problems in each bi-parametric plot). The program code for one fine parameter scan runs approximately 50 times faster on a Tesla K20 GPU (Kepler architecture) than on an Intel i7-4790 4 core CPU even applying double precision floating point operations
