New functionalities in MatCont: delay equations and Lyapunov exponents

MatCont is a powerful MATLAB-based toolbox for numerical bifurcation analysis focussing on smooth ODEs. A user can study equilibria, periodic and connecting orbits, and their stability and bifurcations. Here, we detail and demonstrate the additional functionalities included in version 7p6. The first is a delay equation importer enabling MatCont users to study a much larger class of models, namely delay equations with finite delay, including delay differential and renewal equations. This importer translates the delay equation into a system of ODEs using a pseudospectral approximation with an order specified by the user. We also implemented Lyapunov exponent computations to investigate the presence of chaotic dynamics, event functions for Poincaré maps, and enhanced homoclinic continuation. We demonstrate these features with some step-by-step guided examples, including the well-known Mackey–Glass equation. The new functionalities broaden both the class of models that can be analysed with MatCont and the kind of analyses that can be performed, expanding the tools available to modellers.