Parallel Numerical Creation of 2-parametric Bifurcation Diagram of Nonlinear Oscillators

Abstract

This paper presents the numerical creation of 2-parametric bifurcation diagrams of nonlinear oscillators with a simple iterative algorithm, which can be easily parallelized. The parallel algorithm was tested with two simple well-known nonlinear oscillators, the Van der Pol oscillator and the Duffing-Holmes oscillator. It was examined how the resolution (number of iterations) affects the speedup and the efficiency. The test results show that a relative good speed up with a good efficiency could be achieved even using a simple desktop.

Keywords

• parallel computing
• bifurcation diagram
• numerical analysis
• nonlinear oscillator
• maple