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

作者：Liu F^*; Burrage K

来源：Computers & Mathematics with Applications, 2011, 62(3): 822-833.

DOI：10.1016/j.camwa.2011.03.002

• Parameter estimation
• Fractional dynamical models
• Fractional Predictor-Corrector method
• Hybrid simplex search and particle swarm optimization
• Competence induction

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.

• 出版日期2011-8