### Mathematical definition

A Fold bifurcation of limit cycles (Limit Point of Cycles, LPC) generically corresponds to a turning point of a curve of limit cycles. It can be characterized by adding an extra constraint to (47) where is the Fold test function. The complete BVP defining a LPC point using the minimal extended system is

|  |  | (70)

where is defined by requiring

| (71)

Here is a function, and are scalars and

| (72)

where the bordering functions , vector and scalars and are chosen so that is nonsingular [15]. This method (using system (71) and (72)) is implemented in the curve definition file `limitpointcycle`. The discretization is done using orthogonal collocation in the same way as it was done for limit cycles.