Chaotic behavior in Chern-Simons-Higgs systems

Abstract

We investigate the dynamical behavior of the Chern-Simons-Higgs system, with and without the Maxwell term for the case of spatial homogeneity. The pure Chern-Simons-Higgs system is shown to be integrable. Inclusion of the Maxwell term renders the system chaotic. A Painlev\'e analysis for the Maxwell-Chern-Simons-Higgs (MCSH) system is carried out to indicate its nonintegrability. Numerical studies of the Poincar\'e plots and Lyapunov exponents are used to establish chaotic behavior in the MCSH system.