Herbert Scheingraber

A comparative classification of complexity measures

Abstract A number of different measures of complexity have been described, discussed, and applied to the logistic map. A classification of these measures has been proposed, distinguishing homogeneous and generating partitions in phase space as well as structural and dynamical elements of the considered measure. The specific capabilities of particular measures to detect particular types of behavior of dynamical systems have been investigated and compared with each other.

Complexity and meaning in nonlinear dynamical systems

Measures of complexity and meaning in nonlinear dynamical systems are presented, applied to specific examples, and compared with each other. A basic conceptual and operational equivalence of both kinds of measures is described. This equivalence substantiates earlier indications by Atlan and Grassberger for a close relationship between complexity and meaning. Both concepts are suggested as candidates to demonstrate the necessity of certain extensions and modifications required to update several habitual regulative principles of the exact sciences.

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.

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.

The significance of causally coupled, stable neuronal assemblies for the psychological time arrow

Stable neuronal assemblies are generally regarded as neural correlates of mental representations. Their temporal sequence corresponds to the experience of a direction of time, sometimes called the psychological time arrow. We show that the stability of particular, biophysically motivated models of neuronal assemblies, called coupled map lattices, is supported by causal interactions among neurons and obstructed by non-causal or anti-causal interactions among neurons. This surprising relation between causality and stability suggests that those neuronal assemblies that are stable due to causal neuronal interactions, and thus correlated with mental representations, generate a psychological time arrow. Yet this impact of causal interactions among neurons on the directed sequence of mental representations does not rule out the possibility of mentally less efficacious non-causal or anti-causal interactions among neurons.

Operant Behavior Tests in Rats after Prenatal Exposure to High Frequency Electromagnetic Fields

There is increasing public concern regarding health hazards of exposure to electromagnetic fields (EMFs) (Bernhardt et al. 1997).

From the Dynamics of Coupled Map Lattices to the Psychological Arrow of Time

Stable neuronal assemblies are generally regarded as neural correlates of mental representations. Their temporal sequence corresponds to the experience of a direction of time, sometimes called the psychological time arrow. We show that the stability of particular, biophysically motivated models of neuronal assemblies, called coupled map lattices, is supported by causal interactions among neurons and obstructed by non‐causal or anti‐causal interactions among neurons. This surprising relation between causality and stability suggests that those neuronal assemblies that are stable due to causal neuronal interactions, and thus correlated with mental representations, generate a psychological time arrow. Yet this impact of causal interactions among neurons on the directed sequence of mental representations does not rule out the possibility of mentally less efficacious non‐causal or anti‐causal interactions among neurons.