Modular Neurodynamics and Its Classification by Synchronization Cores.

It is assumed that the cause of cognitive and behavioral capacities of living systems is to be found in the complex structure-function relationship of their brains; a property that is still difficult to decipher. Based on a neurodynamics approach to embodied cognition this paper introduces a method to guide the development of modular neural systems into the direction of enhanced cognitive abilities. It uses formally the synchronization of subnetworks to split the dynamics of coupled systems into synchronized and asynchronous components. The concept of a synchronization core is introduced to represent a whole family of parameterized neurodynamical systems living in a synchronization manifold. It is used to identify those coupled systems having a rich spectrum of dynamical properties. Special coupling structures-called generative-are identified which allow to make the synchronized dynamics more "complex" than the dynamics of the isolated parts. Furthermore, a criterion for coupling structures is given which, in addition to the synchronized dynamics, allows also for an asynchronous dynamics by destabilizing the synchronization manifold. The large class of synchronization equivalent systems contains networks with very different coupling structures and weights allsharing the same dynamical properties. To demonstrate the method a simple example is discussed in detail.

Neurodynamics in the Sensorimotor Loop: Representing Behavior Relevant External Situations.

In the context of the dynamical system approach to cognition and supposing that brains or brain-like systems controlling the behavior of autonomous systems are permanently driven by their sensor signals, the paper approaches the question of neurodynamics in the sensorimotor loop in a purely formal way. This is carefully done by addressing the problem in three steps, using the time-discrete dynamics of standard neural networks and a fiber space representation for better clearness. Furthermore, concepts like meta-transients, parametric stability and dynamical forms are introduced, where meta-transients describe the effect of realistic sensor inputs, parametric stability refers to a class of sensor inputs all generating the "same type" of dynamic behavior, and a dynamical form comprises the corresponding class of parametrized dynamical systems. It is argued that dynamical forms are the essential internal representatives of behavior relevant external situations. Consequently, it is suggested that dynamical forms are the basis for a memory of these situations. Finally, based on the observation that not all brain process have a direct effect on the motor activity, a natural splitting of neurodynamics into vertical (internal) and horizontal (effective) parts is introduced.

Behavior control in the sensorimotor loop with short-term synaptic dynamics induced by self-regulating neurons.

The behavior and skills of living systems depend on the distributed control provided by specialized and highly recurrent neural networks. Learning and memory in these systems is mediated by a set of adaptation mechanisms, known collectively as neuronal plasticity. Translating principles of recurrent neural control and plasticity to artificial agents has seen major strides, but is usually hampered by the complex interactions between the agent's body and its environment. One of the important standing issues is for the agent to support multiple stable states of behavior, so that its behavioral repertoire matches the requirements imposed by these interactions. The agent also must have the capacity to switch between these states in time scales that are comparable to those by which sensory stimulation varies. Achieving this requires a mechanism of short-term memory that allows the neurocontroller to keep track of the recent history of its input, which finds its biological counterpart in short-term synaptic plasticity. This issue is approached here by deriving synaptic dynamics in recurrent neural networks. Neurons are introduced as self-regulating units with a rich repertoire of dynamics. They exhibit homeostatic properties for certain parameter domains, which result in a set of stable states and the required short-term memory. They can also operate as oscillators, which allow them to surpass the level of activity imposed by their homeostatic operation conditions. Neural systems endowed with the derived synaptic dynamics can be utilized for the neural behavior control of autonomous mobile agents. The resulting behavior depends also on the underlying network structure, which is either engineered or developed by evolutionary techniques. The effectiveness of these self-regulating units is demonstrated by controlling locomotion of a hexapod with 18 degrees of freedom, and obstacle-avoidance of a wheel-driven robot.

Deriving neural network controllers from neuro-biological data: implementation of a single-leg stick insect controller.

This article presents modular recurrent neural network controllers for single legs of a biomimetic six-legged robot equipped with standard DC motors. Following arguments of Ekeberg et al. (Arthropod Struct Dev 33:287-300, 2004), completely decentralized and sensori-driven neuro-controllers were derived from neuro-biological data of stick-insects. Parameters of the controllers were either hand-tuned or optimized by an evolutionary algorithm. Employing identical controller structures, qualitatively similar behaviors were achieved for robot and for stick insect simulations. For a wide range of perturbing conditions, as for instance changing ground height or up- and downhill walking, swing as well as stance control were shown to be robust. Behavioral adaptations, like varying locomotion speeds, could be achieved by changes in neural parameters as well as by a mechanical coupling to the environment. To a large extent the simulated walking behavior matched biological data. For example, this was the case for body support force profiles and swing trajectories under varying ground heights. The results suggest that the single-leg controllers are suitable as modules for hexapod controllers, and they might therefore bridge morphological- and behavioral-based approaches to stick insect locomotion control.

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.