Currently, for both SD and constant delays, there is the underlying assumption that these delays are discrete points in time. Many models, however, involve an integral over the past, i.e. some dependence on $\int_{-\tau}^0 K(\theta) x(t + \theta) d\theta$, with $K$ some weighting. One can somewhat 'hack' their way around this by setting the delays to be quadrature nodes, and approximating the integral using a bunch of discrete delays, but I don't know what impact this has on the computed spectrum/other parts of DDEBifurcationKit's algorithms (I would have to read up on the relevant literature).
In either case, given how common distributed delays are in non-linear DDEs, a more convenient interface would be welcome.
In DifferentialEquations.jl, the implementation of the DDE has full access to the history function. Optionally, a set of discrete delays and a set of state-dependent discrete delays can be given as hints to speed up computations. I don't know how feasible it is to use such an interface for bifurcation analysis, but I would think of that as the ideal scenario from an end user perspective.
Either case, I want to close with a quick word of thanks. As far as I can tell, this is the only bifurcation package for DDEs that is both based on a fully FOSS software stack and actively developed, and a quite extensive one at that. Such an effort is invaluable to the DDE community! 🙂
Currently, for both SD and constant delays, there is the underlying assumption that these delays are discrete points in time. Many models, however, involve an integral over the past, i.e. some dependence on$\int_{-\tau}^0 K(\theta) x(t + \theta) d\theta$ , with $K$ some weighting. One can somewhat 'hack' their way around this by setting the delays to be quadrature nodes, and approximating the integral using a bunch of discrete delays, but I don't know what impact this has on the computed spectrum/other parts of DDEBifurcationKit's algorithms (I would have to read up on the relevant literature).
In either case, given how common distributed delays are in non-linear DDEs, a more convenient interface would be welcome.
In DifferentialEquations.jl, the implementation of the DDE has full access to the history function. Optionally, a set of discrete delays and a set of state-dependent discrete delays can be given as hints to speed up computations. I don't know how feasible it is to use such an interface for bifurcation analysis, but I would think of that as the ideal scenario from an end user perspective.
Either case, I want to close with a quick word of thanks. As far as I can tell, this is the only bifurcation package for DDEs that is both based on a fully FOSS software stack and actively developed, and a quite extensive one at that. Such an effort is invaluable to the DDE community! 🙂