444 research outputs found

    The Fractional SIRC Model and Influenza A

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    This paper deals with the fractional-order SIRC model associated with the evolution of influenza A disease in human population. Qualitative dynamics of the model is determined by the basic reproduction number, 0. We give a detailed analysis for the asymptotic stability of disease-free and positive fixed points. Nonstandard finite difference methods have been used to solve and simulate the system of differential equations

    New Existence Results for Fractional Integrodifferential Equations with Nonlocal Integral Boundary Conditions

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    We consider a boundary value problem of fractional integrodifferential equations with new nonlocal integral boundary conditions of the form: x(0)=βx(θ), x(ξ)=α∫η1‍x(s)ds, and 0<θ<ξ<η<1. According to these conditions, the value of the unknown function at the left end point t=0 is proportional to its value at a nonlocal point θ while the value at an arbitrary (local) point ξ is proportional to the contribution due to a substrip of arbitrary length (1-η). These conditions appear in the mathematical modelling of physical problems when different parts (nonlocal points and substrips of arbitrary length) of the domain are involved in the input data for the process under consideration. We discuss the existence of solutions for the given problem by means of the Sadovski fixed point theorem for condensing maps and a fixed point theorem due to O’Regan. Some illustrative examples are also presented

    Multi-input distributed classifiers for synthetic genetic circuits

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    For practical construction of complex synthetic genetic networks able to perform elaborate functions it is important to have a pool of relatively simple "bio-bricks" with different functionality which can be compounded together. To complement engineering of very different existing synthetic genetic devices such as switches, oscillators or logical gates, we propose and develop here a design of synthetic multiple input distributed classifier with learning ability. Proposed classifier will be able to separate multi-input data, which are inseparable for single input classifiers. Additionally, the data classes could potentially occupy the area of any shape in the space of inputs. We study two approaches to classification, including hard and soft classification and confirm the schemes of genetic networks by analytical and numerical results

    Finite-time passivity for neutral-type neural networks with time-varying delays – via auxiliary function-based integral inequalities

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    In this paper, we investigated the problem of the finite-time boundedness and finitetime passivity for neural networks with time-varying delays. A triple, quadrable and five integral terms with the delay information are introduced in the new Lyapunov–Krasovskii functional (LKF). Based on the auxiliary integral inequality, Writinger integral inequality and Jensen’s inequality, several sufficient conditions are derived. Finally, numerical examples are provided to verify the effectiveness of the proposed criterion. There results are compared with the existing results.&nbsp