Symmetries, Resonances, and Second Order Hysteresis

Abstract

This chapter is a continuation of the preceding chapter to two-dimensional systems. We will identify new features of our self-referential dynamical system again independently of any specific embodiment effects. The additional dimension opens the possibility for state oscillations, where the entanglement of state and parameter dynamics will lead to interesting phenomena and induces behavioral variability. The most prominent effects are driving oscillatory systems into a second order hysteresis (by a self-organized frequency sweeping effect) and getting into resonance with latent oscillatory modes of the controlled system.