Sistemas p-fuzzy modificados para dinâmicas populacionais: modelagens e simulações

Abstract

The great challenge of mathematical modeling is to describe natural phenomena in order to make predictions and take decisions. The use of difference equations and ordinary differential equations has been an essential tool in modeling population-related phenomena. The feasibility and applicability of partially fuzzy systems (p-fuzzy) in modeling phenomena described by differential equations have already been studied. The proposal in this work is to present modified p-fuzzy systems (which membership functions are altered by a potency) and in-time modified p-fuzzy systems (in which the membership functions are altered at each iteration in time) which describe a better approximation to the deterministic solutions for some dynamic population models, than the p-fuzzy systems without modifications. The modified p-fuzzy systems were obtained numerically by means of programs in Matlab software, in order to determine the potency and function that adequately alter the potency, calculating the smallest error between the analytic solution and the modified p-fuzzy systems for some models in population dynamics. We verified that in-time modified p-fuzzy system for the pest control model is more convenient in relation to both the p-fuzzy without modifications and the one modified by the potency, since in this system the final result is the smallest pest population that survives to the control. After analyzing the attained results, it can be concluded that when the potency modified p-fuzzy system with either restrictive modifications (potency > 1) or expansive (0 < potency < 1), we accomplish a better approximation for the analytical solution for each model. For the pest control model, this approximation becomes greater when the modification is made to each and a very iteration, i.e., with in-time modified p-fuzzy system.