Inherent global stabilization of unstable local behavior in coupled map lattices

The behavior of two-dimensional coupled map lattices is studied with respect to the global stabilization of unstable local fixed points without external control. It is numerically shown under which circumstances such inherent global stabilization can be achieved for both synchronous and asynchronous updating. Two necessary conditions for inherent global stabilization are derived analytically.Comment: 17 pages, 10 figures, accepted for publication in Int.J.Bif.Chao

Stabilization of causally and non-causally coupled map lattices

Two-dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood. The action of the neighborhood on individual maps can be implemented in terms of "causal" coupling (to spatially distant past states) or "non-causal" coupling (to spatially distant simultaneous states). In this contribution we show that globally stable behavior of coupled map lattices is facilitated by causal coupling, thus indicating a surprising relationship between stability and causality. The influence of causal versus non-causal coupling for synchronous and asynchronous updating as a function of coupling strength and for different neighborhoods is analyzed in detail.Comment: 15 pages, 5 figures, accepted for publication in Physica

Generalized Quantum Theory: Overview and Latest Developments

The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role of proposition observables), and the concept of generalized entanglement. Furthermore, the active role of the observer in the structure of observables and the partitioning of systems is emphasized.Comment: 14 pages, update in reference

Quantum Zeno Features of Bistable Perception

A generalized quantum theoretical framework, not restricted to the validity domain of standard quantum physics, is used to model the dynamics of the bistable perception of ambiguous visual stimuli. The central idea is to treat the perception process in terms of the evolution of an unstable two-state quantum system, yielding a quantum Zeno type of effect. A quantitative relation between the involved time scales is theoretically derived. This relation is found to be satisfied by empirically obtained cognitive time scales relevant for bistable perception.Comment: 19 pages, 1 figur

Weak Quantum Theory: Complementarity and Entanglement in Physics and Beyond

The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of material systems, is outlined and tentatively applied to some examples.Comment: Revised version. Chapter 5.2 (old counting) omitted for separate publication, chapter 5.2 (new counting) reformulate

Stability analysis of coupled map lattices at locally unstable fixed points

Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is difficult to classify and understand. It is therefore desirable to establish analytical tools for exploring fundamental features of CMLs, such as their stability properties. Since CMLs can be considered as graphs, we apply methods of spectral graph theory to analyze their stability at locally unstable fixed points for different updating rules, different coupling scenarios, and different types of neighborhoods. Numerical studies are found to be in excellent agreement with our theoretical results.Comment: 22 pages, 6 figures, accepted for publication in European Physical Journal

Epistemic and Ontic Quantum Realities

Quantum theory has provoked intense discussions about its interpretation since its pioneer days. One of the few scientists who have been continuously engaged in this development from both physical and philosophical perspectives is Carl Friedrich von Weizsaecker. The questions he posed were and are inspiring for many, including the authors of this contribution. Weizsaecker developed Bohr's view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein's ontically oriented position