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

Limits with Oscillating Discontinuities

Limits with Oscillating Discontinuities

An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...

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.

Cyclic Processes And Isolated Systems

Cyclic Processes And Isolated Systems

A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each...

Cell Signaling Feedback Loops

Cell Signaling Feedback Loops

Positive and negative feedback loops are crucial for regulating biological signaling systems. These feedback loops are processes that connect output signals to their inputs.
Negative feedback loops
Most signaling systems have negative feedback loops that can perform different functions such as output limiter, and adaptation.
Output limiter
Upon receiving an input signal, the cellular response rapidly increases until a threshold is reached. Beyond this threshold, a negative feedback loop...

Positive Regulator Molecules

Positive Regulator Molecules

To consistently produce healthy cells, the cell cycle—the process that generates daughter cells—must be precisely regulated.

You might also read

Related Articles

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

Sort by

Same author

[Clinical evaluation of different ophthalmic optical coherence tomography devices using a retinal biomimetic phantom].

[Zhonghua yan ke za zhi] Chinese journal of ophthalmology·2026

Same author

[The application of superselective ophthalmic artery thrombolysis in the treatment of central retinal artery occlusion].

Zhonghua wai ke za zhi [Chinese journal of surgery]·2025

Same author

Extracellular Z-DNA Enhances Cariogenicity of Biofilm.

Journal of dental research·2025

Same author

[Study on the correlation between urinary calcium levels and severity and prognosis of chronic kidney disease].

Zhonghua liu xing bing xue za zhi = Zhonghua liuxingbingxue zazhi·2025

Same author

Zhou et al. Reply.

Physical review letters·2024

Same author

Erratum: Ubiquitous Non-Majorana Zero-Bias Conductance Peaks in Nanowire Devices [Phys. Rev. Lett. 123, 107703 (2019)].

Physical review letters·2024

Search research articles

Related Experiment Video

Updated: Mar 23, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Complex dynamics in biological systems arising from multiple limit cycle bifurcation.

P Yu¹, W Lin²

¹a Department of Applied Mathematics , Western University , London , Ontario Canada.

Journal of Biological Dynamics

|April 5, 2016

Summary

This summary is machine-generated.

This study explores complex dynamics in biological systems using epidemic and predator-prey models. It reveals new forms of bistability, including between equilibrium and oscillations, offering more realistic models.

Keywords:

37L10 37N25 92D30 Dynamical system Hopf bifurcation epidemic model limit cycle normal form predator–prey model stability

More Related Videos

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

Published on: June 9, 2023

Related Experiment Videos

Last Updated: Mar 23, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

Published on: June 9, 2023

Area of Science:

Mathematical Biology
Dynamical Systems Theory
Theoretical Ecology

Background:

Biological systems often exhibit complex dynamics.
Understanding multistability is crucial for realistic modeling.
Bifurcation phenomena can lead to diverse dynamical behaviors.

Purpose of the Study:

To investigate complex dynamical behavior in biological systems.
To demonstrate new types of bistability arising from multiple limit cycles bifurcation.
To provide more realistic models for biological situations.

Main Methods:

Application of bifurcation theory.
Utilizing normal form theory.
Analysis of simple epidemic and predator-prey models.

Main Results:

Exact routes to novel bistability were identified.
Demonstrated bistability between equilibrium and periodic oscillation.
Showcased bistability between two distinct periodic oscillations.

Conclusions:

Multiple limit cycles bifurcation can generate complex multistability.
These findings offer more accurate representations of real-world biological dynamics.
The study provides a theoretical framework for understanding complex biological behaviors.