A numerical continuation software

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

- Continuation of periodic orbits along a parameter
- Calculation of Floquet multipliers of periodic orbits
- Automatic detection of bifurcations
- Continuation of torus, period doubling and fold bifurcations of periodic orbits along two parameters
- Continuation of invariant tori with quasi-periodic orbits along two parameters
- Continuation of steady states (as periodic orbits)

Significant differences from DDE-BIFTOOL

- No need for any programming, equations entered using simple formulae
- Stand-alone software
- Graphical User Interface
- Written in C++, hence faster
- The only software that calculates quasi-periodic tori

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

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

```
vfname()=mackey_glass;
```

time()=t;

period(T)=2.0;

par(a)=-1.0;

par(b)=1.5;

par(tau)=2.0;

DX=delay(X,tau);

dot(X)=a*X + b*DX/(1+DX^10);

init(X)=((1.0-1.5)/(-1.0))^(1.0/10.0);

- 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.

- Mac Application (El Capitan, Intel x86_64)
**Knut-10.dmg** - Windows Installer (Intel 32 bit)
**Knut-10-w32.exe** - Source code
**Knut-10.tar.bz2**

See the **Users' manual**

Dependencies are **OpenBLAS**, **CMake** and optionally **Qt**

To build the software use the following commands:

```
git clone
```**https://github.com/rs1909/knut.git**

cd knut/knut

mkdir build

cd build

../build-unix.sh

make install

On Mac OSX replace the penultimate command with `../build-mac.sh`

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 `../build-win-cross.sh`

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.