Orbit Bifurcations in Nonlinear Oscillator Chains

A chain of nonlinear oscillators prepared in a low-energy, long-wavelength initial condition exhibits recurrent behavior, first observed in a model studied by Fermi, Pasta, Ulam, and Tsingou (FPUT). This phenomenon, known as the metastable state, persists for a long time before the system thermalizes. In the metastable state, the trajectory remains close to a periodic orbit known as a q-breather, which is a coherent structure that is exponentially localized in the space of linear normal modes. We have studied the stability of q-breathers in the α-FPUT system and observed orbit bifurcations that occur when the nonlinearity is varied, due to the non-integrability of the system. This is in contrast with the integrable Toda lattice, where q-breather bifurcations do not occur, and the trajectory remains close to a q-breather indefinitely. We expand the results of our previous work [1] by examining these orbit bifurcations in detail and discussing their role in the breakdown of the metastable state.

[1] Nachiket Karve, Nathan Rose, and David Campbell. Periodic orbits in Fermi-Pasta-Ulam-Tsingou systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(9):093117, 09 2024.