Make bautin_to_subcritical_lc work with SpecialPoint

src/codim2lc/factories.jl

@@ -36,6 +36,9 @@ function FoldLimitCycleProblem(point::AbstractSpecialPoint,
 
     flc_points = special_points(lc_solver,
                                 Codim1LimitCycle.PointTypes.saddle_node)
+    if isempty(flc_points)
+        error("Cannot find fold bifurcation of the limit cycle.")
+    end
     flc_point = resolve_point(flc_points[1], lc_solver)
     if length(flc_points) > 1
         param2 = get(solver.prob.param_axis2, lc_solver.prob.de_prob.p)
@@ -114,14 +117,40 @@ function bautin_to_subcritical_lc(
         solver::Codim2Solver;
         kwargs...)
 
-    point :: SpecialPointInterval  # TODO: support SpecialPoint
     @assert point.point_type == Codim2.PointTypes.bautin
     @assert timekind(point) isa Continuous
 
     solver.prob :: DiffEqCodim2Problem
     de_prob = solver.prob.de_prob :: AbstractODEProblem
     prob_cache = as(solver.cache, ContinuationCache).prob_cache
 
+    if point isa SpecialPoint
+        point = let
+            if point.sweep.value == nothing
+                error("""
+                `point` is not associated with a sweep.
+                point = $(point)
+                 """)
+            end
+            # See: [[../base/solver.jl::SpecialPointInterval]]
+            sweep = as(point.sweep.value, ContinuationSweep)
+            u0 = sweep.u[point.point_index - 1]
+            u1 = sweep.u[point.point_index]
+            _H, J1 = residual_jacobian(u1, prob_cache)
+            SpecialPointInterval(
+                timekind(point),
+                point.point_type,
+                point.point_index,
+                u0,
+                u1,
+                J1,
+                WeakRef(sweep),
+            )
+        end
+    else
+        point :: SpecialPointInterval
+    end
+
     coeff_1 = first_lyapunov_coefficient(prob_cache, point.u1, point.J1)
     if coeff_1 > 0  # u1 is subcritical
         u_sc = point.u1