Frank Pasemann

Complex dynamics and the structure of small neural networks

The discrete-time dynamics of small neural networks is studied empirically, with emphasis laid on non-trivial bifurcation scenarios. For particular two- and three-neuron networks interesting dynamical properties like periodic, quasi-periodic and chaotic attractors are observed, many of them co-existing for one and the same set of parameters. An appropriate equivalence class of networks is defined, describing them as parametrized dynamical systems with identical dynamical capacities. Combined symmetries in phase space and parameter space are shown to generate different representatives of such a class. Moreover, conditions on the connectivity structure are suggested, which guarantee the existence of complex dynamics for a considered equivalence class of network configurations.

SO(2)-networks as neural oscillators

In this paper we present a functional lnoclel of spiking neuron intended for harclware implementation. The model allows the design of speed-and/or area-optimized architectures. Some features of biological spiking neurons are abstracted, while preserving the functionality of the network, in order to define an architecture easily implementable in hardware, mainly in field programmable gate arrays (FPGA). The mnoclel pennits to optimize the architecture following area or speed criteria according to the application. In the same way, several parameters and features are optional, so as to allow more biologically plausible models by increasing the complexity and hardware requirements of the model. We present the results of three example applications performal to verify the computing capabilities of a simple instance of our model.

DYNAMICS OF A SINGLE MODEL NEURON

The parametrized dynamics of a standard nonlinear model neuron with self-interaction is discussed. For units with a self-excitatory connection a hysteresis effect is observed, and the underlying mechanism is identified as that of a cusp catastrophe. This is true for discrete as well as for continuous dynamics. For the discrete dynamics of self-inhibiting units there appear period-doubling bifurcations from stationary states to stable period-2 orbits.

Structure and function of evolved neuro-controllers for autonomous robots

The artificial life approach to evolutionary robotics is used as a fundamental framework for the development of a modular neural control of autonomous mobile robots. The applied evolutionary technique is especially designed to grow different neural structures with complex dynamical properties. This is due to a modular neurodynamics approach to cognitive systems, stating that cognitive processes are the result of interacting dynamical neuro-modules. The evolutionary algorithm is described, and a few examples for the versatility of the procedures are given. Besides solutions for standard tasks like exploration, obstacle avoidance and tropism, also the sequential evolution of morphology and control of a biped is demonstrated. A further example describes the co-evolution of different neuro-controllers co-operating to keep a gravitationally driven art-robot in constant rotation.

Sensor-driven neural control for omnidirectional locomotion and versatile reactive behaviors of walking machines

This article describes modular neural control structures for different walking machines utilizing discrete-time neurodynamics. A simple neural oscillator network serves as a central pattern generator producing the basic rhythmic leg movements. Other modules, like the velocity regulating and the phase switching networks, enable the machines to perform omnidirectional walking as well as reactive behaviors, like obstacle avoidance and different types of tropisms. These behaviors are generated in a sensori-motor loop with respect to appropriate sensor inputs, to which a neural preprocessing is applied. The neuromodules presented are small so that their structure-function relationship can be analysed. The complete controller is general in the sense that it can be easily adapted to different types of even-legged walking machines without changing its internal structure and parameters.

Characterization of periodic attractors in neural ring networks

Abstract The paper presents a discussion of parameterized discrete dynamics of neural ring networks. For specific parameter domains stable periodic orbits coexist. Their periods and the number of orbits of a given period are determined. Even n-rings (i.e., rings with an even number of inhibitory connections) exhibit mainly stable period-n orbits. Odd n-rings display mainly stable period-2n orbits. The dynamical effects of inhibitory connections are analysed, and a characterization of attractors in terms of their “firing pattern” is presented.

Robot Control and the Evolution of Modular Neurodynamics

Summary A modular approach to neural behavior control of autonomous robots is presented. It is based on the assumption that complex internal dynamics of recurrent neural networks can efficiently solve complex behavior tasks. For the development of appropriate neural control structures an evolutionary algorithm is introduced, which is able to generate neuromodules with specific functional properties, as well as the connectivity structure for a modular synthesis of such modules. This so called ENS 3 -algorithm does not use genetic coding. It is primarily designed to develop size and connectivity structure of neuro-controllers. But at the same time it optimizes also parameters of individual networks like synaptic weights and bias terms. For demonstration, evolved networks for the control of miniature Khepera robots are presented. The aim is to develop robust controllers in the sense that neuro-controllers evolved in a simulator show comparably good behavior when loaded to a real robot acting in a physical environment. Discussed examples of such controllers generate obstacle avoidance and phototropic behaviors in non-trivial environments.

Synchronized chaos and other coherent states for two coupled neurons

Abstract The parametrized time-discrete dynamics of two recurrently coupled chaotic neurons is investigated. Basic dynamical features of this system are demonstrated for symmetric couplings of identical neurons. Periodic as well as chaotic orbits constrained to a manifold M of synchronized states are observed. Parameter domains for locally stable synchronization manifolds M are determined by numerical simulations. In addition to the synchronized dynamics there often co-exist periodic, quasiperiodic and even chaotic attractors representing different kinds of non-synchronous coherent dynamics. Simulation results for selected sets of parameters are presented, and synchronization conditions for systems with non-identical neurons are derived. Also these more general systems inherit the above-mentioned dynamical properties.

A simple chaotic neuron

Abstract The discrete dynamics of a dissipative nonlinear model neuron with self-interaction is discussed. For units with self-excitatory connection hysteresis effects, i.e. bistability over certain parameter domains, are observed. Numerical simulations demonstrate that self-inhibitory units with non-zero decay rates exhibit complex dynamics including period-doubling routes to chaos. These units may be used as basic elements for networks with higher-order information processing capabilities.

Synchronization of Internal Neural Rhythms in Multi-Robotic Systems

This paper introduces a method for the coordination of individual action within a group of robots that have to accomplish a common task, gathering energy in a dynamic environment and transferring this energy to a nest. Each individual behavioral pattern is driven by an internal neural rhythm generator exhibiting quasi-periodic oscillations. The paper describes the implementation of this generator, its influence on the dynamics of artificial recurrent neural networks controlling the robots, and the synchronization of internal rhythms with differing frequencies in a group of situated and embodied robots. Synchronization is achieved either by environmental stimuli or even by self-organizing processes solely based on local interactions within a robot population of up to 150 robots. The proposed experimental methodology is used as a bottom-up approach and starting point for answering the question about the complexity required at the individual level to generate sophisticated behavioral patterns at the group level