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

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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]
Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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PubType: Academic Journal
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  Data: <searchLink fieldCode="DE" term="%22Biological+systems%22">Biological systems</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Parameter+estimation%22">Parameter estimation</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+calculus%22">Fractional calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Particle+swarm+optimization%22">Particle swarm optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Systems+biology%22">Systems biology</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
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  Data: 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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  Data: <i>Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.camwa.2011.03.002
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        Text: English
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        PageCount: 12
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        Type: general
      – SubjectFull: Mathematical models
        Type: general
      – SubjectFull: Parameter estimation
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      – SubjectFull: Fractional calculus
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      – SubjectFull: Particle swarm optimization
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      – SubjectFull: Numerical analysis
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              Text: Aug2011
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              Y: 2011
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