Possible Chaotic Behavior in Models Inspired by Field Theories

The Toda Lattice is an exactly integrable three particle system with next neighbor interactions. Its truncations are not integrable and show chaotic behavior. Several of its truncations have been used for astronomical and cosmological models. The Henon-Heiles system is the best-known example, other interesting applications to cosmological models have been developed including the Yang Mills and Yang Mills Higgs systems [1]. Aydıner [2] has studied a chaotic evolution model. String Theory [3], considered as a candidate for a unified theory of everything, suggests that all interactions can be modelled as vibrations of tiny strings. where chaoticity could be modelled by a Higgs field to understand how the symmetry is broken [4]. We also study evolution models, their stability and seek evidence for possible chaotic behavior in the public LIGO and Virgo data on gravitational waves.