I am writing this post to announce a new package MultiParamContinuation.jl in the organisation bifurcationkit. It allows to perform multi parameter continuation of problems in large dimensions. As of now, it only handles the following situation, computing the 2d submanifold defined as

\{ x\in\mathbb R^{n+2}\ |\ F(x) = 0\in\mathbb R^n\}

This is based on the algorithm for Multifario and it is also implemented in the Matlab toolbox COCO.

It is reasonably efficient on StaticArrays and there is an interface to BifurcationKit.jl in order to tackle large scale problems.

Below is a partially computed torus.

I hope some of you will find it useful,

Best regards