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Novel techniques in parameter estimation for fractional dynamical models arising from biological systems

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Bibliographic Details
Title: Novel techniques in parameter estimation for fractional dynamical models arising from biological systems
Authors: Liu, F.1 f.liu@qut.edu.au, Burrage, K.1,2
Source: Computers & Mathematics with Applications. Aug2011, Vol. 62 Issue 3, p822-833. 12p.
Subjects: Biological systems, Mathematical models, Parameter estimation, Fractional calculus, Particle swarm optimization, Systems biology, Numerical analysis
Abstract: Abstract: In recent years, both parameter estimation and fractional calculus have attracted a considerable interest. Parameter estimation of the fractional dynamical models is a new topic. In this paper, we consider novel techniques for parameter estimation of fractional nonlinear dynamical models in systems biology. First, a computationally effective fractional Predictor–Corrector method is proposed for simulating fractional complex dynamical models. Second, we convert the parameter estimation of fractional complex dynamical models into a minimization problem of the unknown parameters. Third, a modified hybrid simplex search (MHSS) and a particle swarm optimization (PSO) is proposed. Finally, these techniques are applied to a dynamical model of competence induction in a cell with measurement error and noisy data. Some numerical results are given that demonstrate the effectiveness of the theoretical analysis. [Copyright &y& Elsevier]
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Database: Engineering Source
Description
Abstract:Abstract: In recent years, both parameter estimation and fractional calculus have attracted a considerable interest. Parameter estimation of the fractional dynamical models is a new topic. In this paper, we consider novel techniques for parameter estimation of fractional nonlinear dynamical models in systems biology. First, a computationally effective fractional Predictor–Corrector method is proposed for simulating fractional complex dynamical models. Second, we convert the parameter estimation of fractional complex dynamical models into a minimization problem of the unknown parameters. Third, a modified hybrid simplex search (MHSS) and a particle swarm optimization (PSO) is proposed. Finally, these techniques are applied to a dynamical model of competence induction in a cell with measurement error and noisy data. Some numerical results are given that demonstrate the effectiveness of the theoretical analysis. [Copyright &y& Elsevier]
ISSN:08981221
DOI:10.1016/j.camwa.2011.03.002