Level IV fugacity model depending on temperature by a periodic control system

A ‘level IV fugacity model’ depending on temperature, to simulate effects of periodic temperature changes on the dynamic distribution of chemical compounds in environmental systems is presented. This model is a continuous time dynamic and periodic control system of a nonsteady-state level IV fugacity model with capacity of fugacity, substance degradation rate, and substance transfer coefficients depending on temperature. Properties of this model as stability and positivity are studied. In order to evaluate the numerical results, a discretization preserving the stability and yielding the positivity of the model is used to simulate and illustrate the dynamic distribution of molinate herbicide in a hypothetical three compartmental environmental system, similar to a paddy field, consisting of air, water and bottom sediment, with four periodic temperature changes. The results show that the discretization preserves the periodicity, stability and the positivity properties. When considering a periodic temperature variation, we observed a significant temperature effect on the capacity of fugacity of compartments of the model. This temperature effect largely affect the dynamic distribution of a chemical compound in environmental systems.