Heliospheric shocks and catastrophe theory

Various configurations of forward and reverse shocks that occur in the outer heliosphere can be classified using catastrophe theory. The existence of a forward shock is associated with a local maximum of a polynomial, and the existence of a reverse shock is associated with a local minimum of a polynomial. A configuration with N forward shocks and N reverse shocks corresponds to a polynomial with N maxima and N minima. The formation of forward and reverse shocks corresponds to the creation of maxima and minima of a polynomial, which is described by the separatrices of the catastrophes. The coalescence of two forward (reverse) shocks corresponds to the situation when two maxima (minima) of a polynomial have equal values, and the interaction of a forward shock with a reverse shock corresponds to a polynomial with a local maximum equal to a local minimum; these situations are described by the Maxwell sets of the appropriate catastrophes.