Abstract

Computational models are generally either stochastic or deterministic (although hybrids, like the chemical langevin also exist). Stochastic models use computational elements that represent the enties and the processes by which they interact and create a procedural algorithm to generate realistic data. Deterministic models use mathematical representations of the underlying regularities that are produced by the entities being modeled and generate theoretically perfect data. Students often find stochastic models useful, especially when a visualization is present that illustrates the entities being modelled. We propose linking a stochastic model with a deterministic model for students to explore the strengths and weaknesses of each. We used Netlogo, Jsim, and Excel to demonstrate how this might work

Introduction

We began with a Netlogo Model of Enzyme Kineticsand a JSim Model of Single substrate-single product reversible enzymic reaction and modified the Netlogo model to match the JSim model as much as possible.

Population Growth

Since Malthus, people have recognized the capacity for populations to expand exponentially. Verhulst recognized that by adding a factor that limited growth at a carrying capacity produced a more realistic outcome -- this has been called the Logistic Growth Equation: a deterministic model that produces a mathematical description of the growth of a population as it approaches carrying capacity. With the creation of computers, it has been possible to use stochastic approaches to modelling populations. In this poster we constrast a stochastic simulation of population growth with two implementations of the Logistic Growth Equation.

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