On a differential system arising in the network control theory

We investigate the three-dimensional dynamical system occurring in the network regulatory systems theory for specific choices of regulatory matrix { { 0, 1, 1 } { 1, 0, 1 } { 1, 1, 0 } } and sigmoidal regulatory function f(z) = 1 / (1 + e-μz), where z = ∑ Wij xj - θ. The description of attracting sets is provided. The attracting sets consist of respectively one, two or three critical points. This depends on whether the parameters (μ,θ) belong to a set Ω or to the complement of Ω or to the boundary of Ω, where Ω is fully defined set

Incremental embodied chaotic exploration of self-organized motor behaviors with proprioceptor adaptation

This paper presents a general and fully dynamic embodied artificial neural system, which incrementally explores and learns motor behaviors through an integrated combination of chaotic search and reflex learning. The former uses adaptive bifurcation to exploit the intrinsic chaotic dynamics arising from neuro-body-environment interactions, while the latter is based around proprioceptor adaptation. The overall iterative search process formed from this combination is shown to have a close relationship to evolutionary methods. The architecture developed here allows realtime goal-directed exploration and learning of the possible motor patterns (e.g., for locomotion) of embodied systems of arbitrary morphology. Examples of its successful application to a simple biomechanical model, a simulated swimming robot, and a simulated quadruped robot are given. The tractability of the biomechanical systems allows detailed analysis of the overall dynamics of the search process. This analysis sheds light on the strong parallels with evolutionary search

Self-stabilizing wormhole routing

Parallel and distributed systems are composed of individual processors that communicate with one another by exchanging messages through communication links. When the sender and the receiver of a message are not direct neighbors, intermediate processors must cooperate to ensure proper routing; Wormhole routing is most common in parallel architectures in which messages are sent in small fragments called flits. We assume that each processor will contain a single fixed-size flit buffer for each incoming link. A processor must forward the flit in a given link buffer to another processor before receiving another flit on that link. This permits messages to wind through the entire network from source to destination, resembling a worm. Wormhole routing is a lightweight and efficient method of routing messages between parallel processors; Our purpose is to modify existing wormhole routing algorithms in familiar topologies to make them self-stabilizing. Self-stabilization is a technique that guarantees tolerance to transient faults (e.g. memory corruption or communication hazard) for a given protocol. Transient faults would typically place the network in an illegitimate state, while Self-stabilization guarantees that the network recovers a correct behavior in finite time, without the need for human intervention. Self-stabilization also guarantees the safety property, meaning that once the network is in a legitimate state, it will remain there until another fault occurs; This paper presents self-stabilizing network algorithms in the wormhole routing model, using the unidirectional ring and the two-dimensional mesh topologies. We chose the ring topology to illustrate the numerous difficulties of self-stabilization in a wormhole routing environment, even in one of the most simple network topologies. We then extend the results of the ring topology to a more complex two-dimensional mesh network

On a Planar Dynamical System Arising in the Network Control Theory

We study the structure of attractors in the two-dimensional dynamical system  that appears in the network control theory. We provide description of the attracting set and follow changes this set suffers under the changes of positive parameters µ and Θ.