No abstract

Abstract. Using discrete-time dynamics of a two neuron network with recurrent connectivity it is shown that for specific parameter configurations the output signals of neurons can be of almost sinusoidal shape. These networks live near the Sacker-Neimark bifurcation set, and are termed SO(2)-networks, because their weight matrices correspond to rotations in the plane. The discretized sinus-shaped waveform is due to the existence of quasi-periodic attractors. It is shown that the frequency of the oscillators can be controlled by only one parameter. Signals from the neurons have a phase shift of π/2 and may be useful for various kinds of applications; for instance controlling the gait of legged robots.

No abstract

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.

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