146 research outputs found

    Response of an Excitatory-Inhibitory Neural Network to External Stimulation: An Application to Image Segmentation

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    Neural network models comprising elements which have exclusively excitatory or inhibitory synapses are capable of a wide range of dynamic behavior, including chaos. In this paper, a simple excitatory-inhibitory neural pair, which forms the building block of larger networks, is subjected to external stimulation. The response shows transition between various types of dynamics, depending upon the magnitude of the stimulus. Coupling such pairs over a local neighborhood in a two-dimensional plane, the resultant network can achieve a satisfactory segmentation of an image into ``object'' and ``background''. Results for synthetic and and ``real-life'' images are given.Comment: 8 pages, latex, 5 figure

    Modelling and control of balance laws with applications to networks

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    In this thesis essentially two types of partial differential equations and their applications to networks are considered. The first system is of hyperbolic type with an additional source term. We consider the control of boundary value problems and investigate stability properties. The tool to analyse stability and exponential decay is Lyapunov functions. The theoretical results are transferred to specific applications, such as electric transmission lines and road networks. The second partial differential equation is of parabolic type and describes the movement of an organism under the influence of certain substances. In literature, this process is known as chemotaxis. The chemotaxis model is extended to networks by introducing coupling conditions which ensure the conservation of mass. We prove existence and uniqueness from a numerical point of view. To ensure stability and positivity for the numerical scheme, a network CFL condition is derived by a detailed computation. Finally, several numerical examples are presented

    Umgebungsbedingungen eines einzelnen aktiven Oszillators in einem eindimensionalen Innenohrmodell

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    SIGLETIB: RN 4852 (85-34) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

    Modelling and control of balance laws with applications to networks

    No full text
    In this thesis essentially two types of partial differential equations and their applications to networks are considered. The first system is of hyperbolic type with an additional source term. We consider the control of boundary value problems and investigate stability properties. The tool to analyse stability and exponential decay is Lyapunov functions. The theoretical results are transferred to specific applications, such as electric transmission lines and road networks. The second partial differential equation is of parabolic type and describes the movement of an organism under the influence of certain substances. In literature, this process is known as chemotaxis. The chemotaxis model is extended to networks by introducing coupling conditions which ensure the conservation of mass. We prove existence and uniqueness from a numerical point of view. To ensure stability and positivity for the numerical scheme, a network CFL condition is derived by a detailed computation. Finally, several numerical examples are presented

    Numerical feedback stabilization with applications to networks

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    The focus is on the numerical consideration of feedback boundary control problems for linear systems of conservation laws including source terms. We explain under which conditions the numerical discretization can be used to design feedback boundary values for network applications such as electric transmission lines or traffic flow systems. Several numerical examples illustrate the properties of the results for different types of networks

    A pedestrian flow model with stochastic velocities: Microscopic and macroscopic approaches

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    We investigate a stochastic model hierarchy for pedestrian flow. Starting from a microscopic social force model, where the pedestrians switch randomly between the two states stop-or-go, we derive an associated macroscopic model of conservation law type. Therefore we use a kinetic mean-field equation and introduce a new problem-oriented closure function. Numerical experiments are presented to compare the above models and to show their similarities.Comment: 23 page
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