Local-Global Interaction on a Phase Space Based on Generative Pointer

Nonlinear dynamical systems show some different motions such as periodic, chaotic or intermittent ones. On-off intermittency is aperiodic switching motion between laminar phases and burst phases. It is observed in critical points with blowout bifurcation. Occurrence of it is sensitive with respect to parameter shifts in conventional systems. In the present paper, an extended dynamical system with an interaction between a global structure and a local motion is proposed. This interaction means a reciprocal definition between a parameter and state variables. The reciprocal definition is induced from the concept of a generative pointer that suggests an extended subobject classifier. Ubiquitous on-off intermittency is observed for a wide range of parameter values when a generative pointer is applied to a Henon map. This fact implies robustness of on-off intermittency against parameter shifts.