MultiModel and MultiSynthesis

In this part, an experimental part of the code is presented and concerns the case of multiple zero of the function provided by the check_root method exists. In this case, multiple singular arc can occur.

First, let introduce an exemple of model where there exists multiple zero of the function.

using Filtration
using Plots

e(m,p)  = exp(-m - sin(m)^2)

ff(m,p) = 1/(m+1)
fb(m,p) = -m
ef(m,p) = e(m,p)
eb(m,p) = -e(m,p)
gf(m,p) = 1.
gb(m,p) = 1.

plt_root = check_root(ef, eb, ff, fb, [1.], :max, initial_guess = [0.5, 2, 2.5], xlim = (0, 5), linewidth = 2, label = "Real")

As we can see, there exists multiple zero of the plotted function. An experimental code is developped to provide the synthesis associaated to this kind of model.

ylim = (0, 5); xlim = (0, 10)
multimodel = MultiModel(ef, eb, ff, fb, [1.], :max, [0.5, 2, 2.5]);
multisynthesis = MultiSynthesis(multimodel, xlim, ylim)
plt = plot(multisynthesis, xlim = xlim, ylim = ylim, xlabel = "Time (t)", ylabel = "Mass (m)")