Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Classification of Systems-I01:26

Classification of Systems-I

424
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
424
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

234
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
234
Nonlinear Pharmacokinetics: Causes of Nonlinearity01:22

Nonlinear Pharmacokinetics: Causes of Nonlinearity

473
Nonlinearity in drug pharmacokinetics is caused by various factors influencing how a drug is absorbed, distributed, metabolized, and excreted. Understanding these nonlinear processes is crucial for predicting drug behavior in the body and optimizing drug dosing regimens.
Nonlinear drug absorption can occur when the process is rate-limited by solubility, carrier-mediated transport systems, or saturation of the presystemic gut wall or hepatic metabolism. For instance, high doses of riboflavin...
473
Nonlinear Pharmacokinetics: Overview01:19

Nonlinear Pharmacokinetics: Overview

773
Nonlinear or dose-dependent pharmacokinetics is a phenomenon that occurs when the pharmacokinetic parameters of certain drugs deviate from linear pharmacokinetics at higher doses. These drugs do not follow the expected first-order kinetics, where the rate of drug elimination is directly proportional to the drug concentration. Instead, they exhibit a nonlinear relationship, which can be attributed to several factors.
Nonlinearity can arise due to the saturation of plasma protein-binding or...
773
Feedback control systems01:26

Feedback control systems

550
Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
550
State Space Representation01:27

State Space Representation

359
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
359

You might also read

Related Articles

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

Sort by
Same author

Consequences of Dale's law on the stability-complexity relationship of random neural networks.

Physical review. E·2020
Same author

Exact relations between multifractal exponents at the Anderson transition.

Physical review letters·2006
Same author

Reducing nonideal to ideal coupling in random matrix description of chaotic scattering: application to the time-delay problem.

Physical review. E, Statistical, nonlinear, and soft matter physics·2001
See all related articles

Related Experiment Video

Updated: Nov 12, 2025

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
15:06

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

Published on: January 3, 2016

13.1K

Nonlinearity-generated resilience in large complex systems.

S Belga Fedeli1, Y V Fyodorov1,2, J R Ipsen3

  • 1Department of Mathematics, King's College London, London WC2R 2LS, England, United Kingdom.

Physical Review. E
|March 19, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a nonlinear extension to May's model, revealing a "resilience gap" around stable fixed points. Systems near tipping points lose this resilience, becoming sensitive to displacements.

More Related Videos

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

915
Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

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

Published on: December 7, 2021

2.4K

Related Experiment Videos

Last Updated: Nov 12, 2025

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
15:06

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

Published on: January 3, 2016

13.1K
Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

915
Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

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

Published on: December 7, 2021

2.4K

Area of Science:

  • Ecology
  • Dynamical Systems Theory
  • Mathematical Biology

Background:

  • Robert May's 1972 model is a foundational concept in ecology for understanding ecosystem stability.
  • Nonlinear dynamics and higher-order terms are crucial for a comprehensive analysis of complex systems.
  • Understanding system resilience is vital for predicting responses to environmental changes.

Purpose of the Study:

  • To investigate the resilience of a generalized nonlinear ecological model.
  • To analyze the impact of higher-order terms and random coefficients on system dynamics.
  • To identify mechanisms underlying changes in system resilience near critical thresholds.

Main Methods:

  • Extension of May's 1972 model to include all higher-order nonlinear terms.
  • Incorporation of random Gaussian coefficients in the model expansion.
  • Mathematical analysis of fixed points and their stability around the origin.

Main Results:

  • A "resilience gap" (a region devoid of other fixed points) exists around a stable origin.
  • The radius of this resilience gap vanishes as the origin loses stability (approaching a tipping point).
  • The number of fixed points grows exponentially with system complexity (N) beyond the resilience radius.

Conclusions:

  • Stable systems exhibit inherent resilience to small perturbations due to the "resilience gap".
  • Systems nearing instability lose their resilience gap, becoming more susceptible to disturbances.
  • Complex systems display heightened sensitivity to larger perturbations as the number of fixed points increases nonlinearly.