2019/09/21 by Peter Schmelcher · 1 citation
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Crossover #Exponent #Gravitational singularity #Logarithm #Multistability #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Phase space #Phase transition #Power (physics) #Power law #nlin.CD #physics.class-ph
paper · pdf · doi:10.1088/1751-8121/ab63a6
published as Journal of Physics A 53, 075701 (2020)
arxiv created 2019/09/21 · openalex created_date 2019/09/26 · openalex publication_date 2019/12/18 · arxiv updated 2021/05/25 · openalex updated_date 2026/08/05
Abstract The superexponential self-interacting oscillator (SSO) is introduced and analyzed. Its power law potential is characterized by the dependence of both the base and the exponent on the dynamical variable of the oscillator. Opposite to standard oscillators such as the (an-)harmonic oscillator the SSO combines both scattering and confined periodic motion with an exponentially varying nonlinearity. The SSO potential exhibits a transition point with a hierarchy of singularities of logarithmic and power law character leaving their fingerprints in the agglomeration of its phase space curves. The period of the SSO consequently undergoes a crossover from decreasing linear to a nonlinearly increasing behaviour when passing the transition energy. We explore its dynamics and show that the crossover involves a kick-like behaviour. A symmetric double well variant of the SSO is briefly discussed.