Delay, noise and phase locking in pulse coupled neural networks.

This paper studies the effect of several delay times and noise on the stability of the phase-locked state in the lighthouse model and the integrate and fire model of a pulse coupled neural network. The coupling between neurons may be arbitrary. In both models the increase of delay times leads to a weakening of the stability and to the occurrence of relaxation oscillations.

The cardiovascular system as coupled oscillators?

Based on physiological knowledge, and on an analysis of signals related to its dynamics, we propose a model of the cardiovascular system. It consists of coupled oscillators. Each of them describes one of the subsystems involved in the regulation of one passage of blood through the circulatory system. The flow of blood through the system of closed tubes-the blood vessels-is described by wave equations.

Reversible transitions between synchronization states of the cardiorespiratory system.

Phase synchronization between cardiac and respiratory oscillations is investigated during anesthesia in rats. Synchrograms and time evolution of synchronization indices are used to show that the system passes reversibly through a sequence of different phase-synchronized states as the anesthesia level changes, indicating that it can undergo phase transitionlike phenomena. It appears that the synchronization state may be used to characterize the depth of anesthesia.

A synergetic model for the verbal transformation effect.

We describe a nonlinear dynamical model based on synergetics for the auditory perceptual illusion known as the verbal transformation effect. The model is an extension of a synergetic model of perceptual oscillations of visual ambiguous figures. The main extension is connected to the number of reported alternative phonemic structures, which is typically much greater than the two or three alternatives usually reported in experiments with visual ambiguous figures. The properties of the model, which are derived using basic psychophysical principles, are presented and evaluated on the basis of the fit to earlier empirical work. It will be shown that there is very good agreement between the empirically observed properties of the verbal transformation effect and the properties detected by the model.

Noise in the brain: a physical network model.

In the brain as in any other open physical systems, noise is inevitable. We present an explicit model of an active physical system that is borrowed from laser physics and allows us to establish the properties of the fluctuating forces that cause noise in the system. It is shown how the cooperation of the individual parts of a system (atoms or neurons) can considerably reduce the noise level. In particular we determine the correlation function between the individual parts. The basic equations can be transformed in such a way that a close analogy with typical equations of neural nets are obtained. In particular, the nonlinear properties of neurons described by the sigmoid function are well captured. Propagation of excitation in axons and dendrites is represented by a linear equation, where we consider both a bandwidth filter and more or less free propagation. In the latter case, a close analogy with an equation for neural activity in the sense of Nunez and established by Jirsa and Haken is pointed out.

Extending the HKB model of coordinated movement to oscillators with different eigenfrequencies.

We study the dynamics of a system of coupled nonlinear oscillators that has been used to model coordinated human movement behavior. In contrast to earlier work we examine the case where the two component oscillators have different eigenfrequencies. Problems related to the decomposition of a time series (from an experiment) into amplitude and phase are discussed. We show that oscillations at multiples of the main frequency of the oscillator system may occur in the phase and amplitude due to the choice of a coordinate system and how these oscillations can be eliminated. We derive an explicit equation for the dynamics of the relative phase of the oscillator system in phase space that enables a direct comparison between theory and experiment.

Synchronized oscillations in the visual cortex--a synergetic model.

We present an oscillator network model for the synchronization of oscillatory neuronal activity underlying visual processing. The single neuron is modeled by means of a limit cycle oscillator with an eigenfrequency corresponding to visual stimulation. The eigenfrequency may be time dependent. The mutual coupling strengths are unsymmetrical and activity dependent, and they scatter within the network. Synchronized clusters (groups) of neurons emerge in the network due to the visual stimulation. The different clusters correspond to different visual stimuli. There is no limitation of the number of stimuli. Distinct clusters do not perturb each other, although the coupling strength between all model neurons is of the same order of magnitude. Our analysis is not restricted to weak coupling strength. The scatter of the couplings causes shifts of the cluster frequencies. The model's behavior is compared with the experimental findings. The coupling mechanism is extended in order to model the influence of bicucullin upon the neural network. We additionally investigate repulsive couplings, which lead to constant phase differences between clusters of the same frequency. Finally, we consider the problem of selective attention from the viewpoint of our model.

Vergence eye movement control and multivalent perception of autostereograms.

We introduce a dynamical model for automatic vergence eye movement control. In connection with our dynamical system of binocular model neurons that solves the correspondence problem of stereo-vision, we present a complete model for stereo-vision. Our automatic vergence eye movement control adjusts an image segment, which is of momentary interest to the observer. The adjustment is done in such a way that we only need to define a disparity search range of minimal extension. Recently, a new method of encoding (3D) three-dimensional information in 2D pictures was designed in the form of computer-generated patterns of colored dots. At first glimpse, these so-called autostereograms appear as structured but meaningless patterns. After a certain period of observation, a 3D pattern emerges suddenly in an impressive way. Applying our algorithm to autostereograms, we find a fully satisfactory agreement with the multivalent perception experienced by humans. As in nature, in our model the phase transition between the initial state and the 3D perception state takes place in a very short time. Our algorithm is very robust against noise, and there is no need to interpolate a sparse depth map.

A theoretical model of phase transitions in the human brain.

An experiment using a multisensor SQUID (superconducting quantum interference device) array was performed by Kelso and colleagues (1992) which combined information from three different sources: perception, motor response, and brain signals. When an acoustic stimulus frequency is changed systematically, a spontaneous transition in coordination occurs at a critical frequency in both motor behavior and brain signals. Qualitatively analogous transitions are known for physical and biological systems such as changes in the coordination of human hand movements (Kelso 1981, 1984). In this paper we develop a theoretical model based on methods from the interdisciplinary field of synergetics (Haken 1983, 1987) and nonlinear oscillator theory that reproduces the main experimental features very well and suggests a formulation of a fundamental biophysical coupling.

Stereo vision by self-organization.

We propose a new algorithm for stereoscopic depth perception, where the depth map is the momentary state of a dynamic process. To each image point we assign a set of possible disparity values. In a dynamic process with competition and cooperation, the correct disparity value is selected for each image point. Therefore, we solve the correspondence problem by a dynamic, self-organizing process, the structure of which shows analogies to the human visual system. The algorithm can be implemented in a massive parallel manner and yields good results for either artificial or natural images.