Matcont

Abstract

MATCONT is a graphical MATLAB software package for the interactive numerical study of dynamical systems. It allows one to compute curves of equilibria, limit points, Hopf points, limit cycles, period doubling bifurcation points of limit cycles, and fold bifurcation points of limit cycles. All curves are computed by the same function that implements a prediction-correction continuation algorithm based on the Moore-Penrose matrix pseudo-inverse. The continuation of bifurcation points of equilibria and limit cycles is based on bordering methods and minimally extended systems. Hence no additional unknowns such as singular vectors and eigenvectors are used and no artificial sparsity in the systems is created. The sparsity of the discretized systems for the computation of limit cycles and their bifurcation points is exploited by using the standard Matlab sparse matrix methods. The MATLAB environment makes the standard MATLAB Ordinary Differential Equations (ODE) Suite interactively available and provides computational and visualization tools; it also eliminates the compilation stage and so makes installation straightforward. Compared to other packages such as AUTO and CONTENT, adding a new type of curves is easy in the MATLAB environment. We illustrate this by a detailed description of the limit point curve type.

A mean-field approach to elastically coupled hair bundles

“…Note, the resulting system can also be viewed as the BRN in the limit of infinite N . Both bifurcation diagrams were obtained numerically with the help of the software package MAT-CONT [34], which allows for parameter continuation of equilibrium states and periodic orbits of autonomous systems of ODEs. Both systems show analogous regions in their bifurcation diagram.…”

On the nonlinear dynamics of a rotor in autorotation: a combined experimental and numerical approach

“…There are several freely available continuation software with different levels of maturity and robustness. AUTO [37], Continuation Core (COCO) [38], MATCONT [39] and CL_MATCONT [39] are examples of the most widely used packages. In this analysis, the continuation and bifurcation software AUTO was used.…”

Numerical continuation in classical mechanics and thermodynamics

“…Monitoring the jacobian of br-i is crucial for forecasting these new emerging branches that can be continuated by means of sophisticated strategies 11 . In the absence of such techniques, we simply explore the presence of new solutions by inspection, i.e., using Newton's method for α − < α < α + or α > α + to detect br-ii or br-iii, respectively, starting the iteration from different initial guesses until a new solution branch is identified.…”