| dc.description |
One of the well-known models of biochemical networks is the Goodwin model.
The model describes an oscillatory behavior in an enzymatic control process which is
expressed in a set of nonlinear ordinary differential equations and is often associated with
biochemical experiments containing uncertainties in data measurements. These
uncertainties are possibly either due to limitations of available data, complexity of the
networks, or environmental or demographic changes. In view of these possible
uncertainties, in this paper we shall study solutions of the Goodwin model that is
considered as a fuzzy initial value problem. Three types of fuzzy differential solutions
are discussed: Hukuhara differential and its generalization, and fuzzy differential
inclusions. Applications of fuzzy arithmetic to those types lead into the alpha-cut
deterministic systems, which are then solved by the Runge-Kutta method. Among those
three types, the fuzzy differential inclusions is able to capture oscillatory behavior as the
Goodwin model should have. Taking the benefit from the fuzzy differential inclusions
method, we then demonstrate how to estimate parameters of the model when uncertainty
gets involved in the equation. As an illustration, we apply the method to our generated
fuzzy simulation data and calculate parameters using nonlinear least square method.
Keywords: Fuzzy initial value problems, fuzzy arithmetic, alpha-cut deterministic
systems, Hukuhara differential, generalized Hukuhara differential, fuzzy differential
inclusions. |
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