ANALYSIS OF BIFURCATIONS AND STABILITY PROPERTIES OF MOLECULAR-SYSTEMS

Abstract

The dynamics and stability of a three-dimensional model of dissipative molecular systems are studied in detail. The model considered is produced by an approximate quantum formulation, and it contains two parameters. It has been demonstrated analytically that the system exhibits 'cusp catastrophe' as in the case of potential systems; however, the non-potential nature of the dissipative model is reflected by the existence of limit cycles bifurcating from the equilibrium surface. The critical lines in the parameter plane and the family of limit cycles bifurcating from equilibria are determined analytically, and it has been shown that they are unstable.