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Quadratic Map

Bifurcation diagrams are used in the study of dynamical systems and are applicable to a wide range of fields: from the modeling of biological populations and financial systems to the modeling of chemical reactions and nonlinear circuits, to mention a few.

We have developed a new tool for students and researchers interested in Nonlinear Dynamical Systems, called the Bifurcation Diagrams Explorer. It is available at


This tool lets you explore many of the bifurcation diagrams found in the literature, providing a visualization of the underlying behavior of a dynamical system as a parameter c is changed. We assume that you have a basic knowledge of bifurcation diagrams and dynamical systems.

The tool is powered by our Minerazzi Grapher, a lightweight PHP class that generates all kind of graphs through a web browser. No additional libraries or software needed. A great resource for introducing users to Chaos Theory.