SOME REMARKS ON CORRELATIONS BETWEEN CONFLICT AND INSTABILITY

A study of the stability of classical systems under the influence of t wo conflicting single-well, single-variable potentials is presented. T he control parameters are a so-called conflict parameter c, the distan ce between the two conflicting attractors, and an asymmetry parameter a which determines the relative strength of the two attractors. For co nvex potentials, the influence of conflict on the system stability dep ends on the sign of the third derivative of the conflicting potential functions, resulting in two categories called U-and V-type potentials. The introduction of a concave branch (bias) in convex conflicting pot entials qualitatively changes the system behavior, by generating bifur cation and discontinuity. The cusp catastrophe can be redefined as the conflict between two such biased single-well potentials. The main int erest of the new representation potentially lies in the evocative powe r of the control parameters a and c. The mapping of(a,c) on (u,v), the traditional control parameters of the cusp catastrophe, is given. The cusp develops above a certain critical value of the conflict paramete r c.