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Related Concept Videos

Mechanistic Models: Overview of Compartment Models01:21

Mechanistic Models: Overview of Compartment Models

Mechanistic models, a category encompassing both physiological and compartmental modeling, differ from empirical models' approaches to incorporating known factors about the systems being modeled. Empirical models describe data with minimal assumptions, while mechanistic models aim to provide a robust description of available data by specifying assumptions and integrating known factors about the system. Compartmental analysis is a key example of a mechanistic model in pharmacokinetics and...
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
Growth Models with Integration: Problem Solving01:27

Growth Models with Integration: Problem Solving

In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
Dynamic Equilibrium02:20

Dynamic Equilibrium

A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Compartment Models: Single-Compartment Model01:14

Compartment Models: Single-Compartment Model

The single-compartment model serves as a simplified representation of the human body. This model assumes that the body functions as a single, well-mixed open compartment. When a drug is administered intravenously, it enters the body and quickly distributes uniformly. The drug then undergoes biotransformation and elimination, ultimately leaving the body. The volume of this compartment is referred to as the apparent volume of distribution into which the drug can uniformly distribute. In this...

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Related Experiment Videos

Endogenous Business Cycle Dynamics within Metzlers Inventory Model: Adding an Inventory Floor.

Irina Sushko1, Michael Wegener, Frank Westerhoff

  • 1University of Bamberg, Department of Economics, Feldkirchenstrasse 21, Bamberg, D-96045, Germany.

Nonlinear Dynamics, Psychology, and Life Sciences
|March 31, 2009
PubMed
Summary
This summary is machine-generated.

Metzlers inventory model is enhanced by introducing a floor for inventory levels. This modification allows for stable, periodic business cycle dynamics, improving economic models.

Related Experiment Videos

Area of Science:

  • Economics
  • Mathematical Economics
  • Business Cycle Analysis

Background:

  • The original Metzlers inventory model can generate unstable economic fluctuations.
  • Unrealistic negative inventory levels arise in some model parameters.
  • Understanding business cycle dynamics is crucial for economic stability.

Purpose of the Study:

  • To reformulate Metzlers inventory model to address its limitations.
  • To investigate the impact of a minimum inventory level on economic cycles.
  • To explore new mechanisms for endogenous business cycle generation.

Main Methods:

  • Modification of Metzlers inventory model by introducing a floor constraint.
  • Analysis of the reformulated piecewise linear model.
  • Application of bifurcation theory to identify dynamic regimes.

Main Results:

  • The modified model prevents unrealistic negative inventory levels.
  • A center bifurcation is identified as a trigger for endogenous dynamics.
  • The model now generates stable, quasi-periodic production fluctuations for specific parameters.

Conclusions:

  • The floor constraint stabilizes the Metzlers inventory model.
  • The reformulated model offers a more realistic representation of business cycles.
  • This approach enhances the understanding of endogenous economic fluctuations.