a step-by-step algorithm for plotting local bifurcation diagram

This paper proposes a graphically step-by-step algorithm for plotting local bifurcation diagram as well as determining stability or instability of all branches. The presented method which consists of eight steps, is effortlessly Applicable to the first and second order complex nonlinear systems. It provides a visual sense for engineers to analyze and design systems. The method is validated by applying on several different examples.