A numerical continuation software

View the Project on GitHub rs1909/knut


The software is designed to analyse explicitly time-dependent delay-differential equations with time dependent delays of the form \[ \boldsymbol{M}\,\dot{\boldsymbol{x}}(t) = \boldsymbol{f} (t, \boldsymbol{x}(t-\tau_0(t)), \boldsymbol{x}(t - \tau_1(t)), \dots , \boldsymbol{x}(t - \tau_m(t))) \] The mass matrix $\boldsymbol{M}$ can be singular, hence Knut can handle algebraic equations and neutral delay-differential equations. State dependent delays are not yet supported, see DDE-BIFTOOL for that.

The features include

Significant differences from DDE-BIFTOOL

The Graphical User Interface also includes a plotting tool that displays the calculation live.

Sample equation specification

The Mackey-Glass equation \[\dot{x} ( t ) = ax ( t ) + b \frac{x ( t - \tau )}{1 + x^{10} ( t - \tau )}\] is represented by the following code

Bifurcation diagram of the Mackey-Glass equation

Bifurcation diagram

    Figure 1. Fold bifurcations of the period-two orbits. Black curves are periodic solutions continued along $b=$constant lines. Red curves refer to fold bifurcations, and the blue line is the period doubling curve, where the period-two orbits arise.

Package downloads


See the Users' manual

Compilation instructions

Dependencies are OpenBLAS, CMake and optionally Qt

To build the software use the following commands:

On Mac OSX replace the penultimate command with ../
To make an installable package use make install and make dmg which will produce a disk image

On Fedora Linux with the MinGW cross-compiler installed the ../ will compile the software for Windows. To make a package use makensis wininstaller.nsi.

Please report any bugs and wishes on the issue tracker, I'll try to address them as my time allows it.