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    Study of kinetic model for fungal spore germination under dynamic conditions: Case study on germination of Penicillium expansum spores
    (2023-12-01)
    Boonruang, Panuluk
    ;
    Lerkkasemsan, Nuttapol
    The germination of fungal spores under non-isothermal conditions has been studied for several years, however, no mathematical model has been able to describe them suitably. Therefore, in this paper, we developed a new model to clarify the understanding of fungal spore germination under non-isothermal conditions by considering the effects of magnitude of condition change and difference in phase of spore during condition change on kinetic parameters, i.e., the mean rate of germination (μ) and the time that half of spores had germinated (t<inf>h</inf>). To combine both effects into our new model, it was necessary to develop other two new models. The first model was used for estimating the swelling time of spores. The second model was the relationship between t<inf>h</inf> vs μ. After we had completed both models and successfully combined both effects into the new model for fungal spore germination under non-isothermal conditions, the new model was validated against experimental data on germination of Penicillium expansum spores in the literature. The prediction results showed that the new model well described the germination of this fungus under non-isothermal conditions.
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    Dynamic of logistic model at fractional order
    (2009-12-01)
    Suansook, Yoothana
    ;
    Paithoonwattanakij, Kitti
    In this paper we have obtain the generalized form of the logistic model to arbitrary order using fractional calculus. The model is explained the population growth. The discrete version of the model have important role in studying the chaotic dynamic. The fractional calculus is feasible to evaluate the differential and integral of non integer order. This mathematical subject is helping fine tune analysis the chaotic properties of the logistic model. The numerical results show the Lyapunov exponent at various fractional orders. The positive Lyapunov exponent is indicate that the system is chaotic at fractional order. The periodic solutions of half fractional order are also present. ©2009 IEEE.