Modelagem matemática de circuitos elétricos equivalentes em plantas

Abstract

Electrical signals in plants are one of the forms of internal signaling between their different parts, and they are generated by the unbalance of the ions present on both sides of the membrane. These signals can be modeled through equivalent electrical circuits electrically stimulated by different mathematical functions, which are a tool to evaluate the stimulus and response mechanisms between different parts of the plants. In this work, the objective is to study models of equivalent electrical circuits for electrical signals in plants, proposing analogies between the electrical components presente in the circuits and the plant structures. Two models of equivalent electric circuits will be studied, the first is a change in the mathematical model of equivalent electric circuit for Aloe Vera, presented by (VOLKOV; SHTESSEL, 2016), which proposes constant values for capacitances. The modification of this model considers that the capacitance values vary according to the electrical potentials, since they represent the ionic channels and the passage of ions through the channels varies according to the potentials on both sides of the membranes. The second model is the proposal of an equivalente electrical circuit for electrical signaling between the internal and external environment of the cells. From the study carried out in the proposed model, the theory of linear optimal control is applied, in order to represent the action of the electrogenic pumps, which are protein complexes that regulate the activity of H+ ions. Through numerical results obtained from the mathematical modeling of the electrical circuits studied, we will show what the alteration of the first model causes in the time paths and the results of the proposed model with and without control application.