Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Modeling with Differential Equations

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

Population Growth

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.

Exponential Equations for Modeling Growth

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...

Growth Models with Integration: Problem Solving

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...

Geometric Sequences

Geometric Sequences

In systems where values diminish by a constant proportion at each stage, the resulting sequence follows a geometric structure. Each new value in the sequence is obtained by applying a fixed multiplier to the preceding term. This regular, proportional decline type is often used to represent processes involving gradual loss, such as energy dissipation or reduction in amplitude over time.When analyzing the total effect of such a process across unlimited iterations, the series of values is referred...

Exponential Growth

Exponential Growth

Bacterial populations exhibit exponential growth when conditions such as nutrient availability and temperature are favorable. In this phase, cells reproduce through binary fission, where each cell divides into two identical daughter cells. This process causes the population to double at regular intervals, resulting in a growth rate that is directly proportional to the current number of cells. As the population increases, the number of new cells formed during each generation also grows, creating...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Graph-Theoretical Approach for Predicting Physicochemical Properties of Stiff-Person Syndrome Drugs.

ChemistryOpen·2026

Same author

Fault-tolerant partition resolvability of cycle with chord.

PloS one·2024

Same author

Opinion formation in multiplex networks with general initial distributions.

Scientific reports·2018

Same author

Groupies in multitype random graphs.

SpringerPlus·2016

Search research articles

Related Experiment Video

Updated: May 2, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Geometric assortative growth model for small-world networks.

¹Singapore University of Technology and Design, Singapore 138682 ; Institute for Cyber Security, University of Texas at San Antonio, TX 78249, USA.

Thescientificworldjournal

|March 1, 2014

Summary

This summary is machine-generated.

We introduce a new geometric model for small-world networks, demonstrating tunable small-world properties and assortative mixing. This model offers analytical solutions for key network topological characteristics.

More Related Videos

Precise, High-throughput Analysis of Bacterial Growth

Precise, High-throughput Analysis of Bacterial Growth

Published on: September 19, 2017

Monitoring Spatial Segregation in Surface Colonizing Microbial Populations

Monitoring Spatial Segregation in Surface Colonizing Microbial Populations

Published on: October 29, 2016

Related Experiment Videos

Last Updated: May 2, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Precise, High-throughput Analysis of Bacterial Growth

Precise, High-throughput Analysis of Bacterial Growth

Published on: September 19, 2017

Monitoring Spatial Segregation in Surface Colonizing Microbial Populations

Monitoring Spatial Segregation in Surface Colonizing Microbial Populations

Published on: October 29, 2016

Area of Science:

Network Science
Graph Theory
Complex Systems

Background:

Natural and human-made networks often exhibit small-world phenomena and assortative mixing.
Understanding these network properties is crucial for various scientific disciplines.

Purpose of the Study:

To propose a novel geometrically growing model for small-world networks.
To demonstrate that the proposed model allows for tunable small-world phenomenon and assortativity.
To derive analytical solutions for key topological properties of the generated networks.

Main Methods:

Development of a geometrically growing network model.
Analytical derivation of topological properties including order, size, degree distribution, degree correlation, clustering, transitivity, and diameter.
Exploration of the model's relationship to Farey graph construction.

Main Results:

The proposed model successfully generates networks with tunable small-world characteristics.
The model exhibits tunable assortative mixing.
Analytical solutions for fundamental network topological properties were obtained.
The model serves as a generalization for iterative Farey graph construction.

Conclusions:

The proposed geometric model provides a flexible framework for studying small-world networks.
The model's ability to tune small-world properties and assortativity offers insights into network organization.
The analytical tractability of the model facilitates deeper understanding of network topology.