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

Multimachine Stability

Multimachine Stability

Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:

The Swing Equation

The Swing Equation

The Swing Equation is a fundamental tool in power system dynamics, especially for analyzing the behavior of generating units like three-phase synchronous generators. This equation emerges from applying Newton's second law to the rotor of a generator, encompassing factors such as inertia, angular acceleration, and the interplay between mechanical and electrical torques.
In a steady-state operation, the mechanical torque (Τm) supplied to the generator is balanced by the electrical torque (Τe)...

Classification of Systems-I

Classification of Systems-I

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:

Stability of Equilibrium Configuration: Problem Solving

Stability of Equilibrium Configuration: Problem Solving

The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...

Second Order systems I

Second Order systems I

A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...

Second Order systems II

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If ζ...

You might also read

Related Articles

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

Sort by

Same author

Symmetry-breaking, grouped images and multistability with transient unconsciousness.

Nonlinear dynamics, psychology, and life sciences·2013

Same author

Decision making with complex nonlinear systems: inference and identification in the context of DS22q11.2.

Nonlinear dynamics, psychology, and life sciences·2013

Same author

Brain dynamics and conscious sequencing.

Nonlinear dynamics, psychology, and life sciences·2011

Same author

Multistable switching series in chaotic nets.

Nonlinear dynamics, psychology, and life sciences·2011

Same author

Conceptual problems in cardiological prediction.

Nonlinear dynamics, psychology, and life sciences·2009

Same author

Introduction to nonlinear methodology part 2: domain-specific problems.

Nonlinear dynamics, psychology, and life sciences·2006

Search research articles

Related Experiment Video

Updated: Jun 14, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

The Sheperd equation and chaos identification.

Robert A M Gregson¹

¹Department of Psychology, Australian National University, CVanberra, ACT 0200, Australia. ramgdd@bigpond.com

Nonlinear Dynamics, Psychology, and Life Sciences

|March 30, 2010

Summary

This summary is machine-generated.

Sheperd's (1982) fish population model reveals complex dynamics like periodicity and chaos. This equation shows potential applications beyond fisheries, possibly in psychophysiological studies.

Related Experiment Videos

Last Updated: Jun 14, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Ecology
Mathematical Biology
Psychophysiology

Background:

The Sheperd model (1982) was initially developed to analyze stability in exploited fish populations.
Ecological models often exhibit complex dynamics that can inform other scientific fields.

Purpose of the Study:

To explore the broader applicability of Sheperd's (1982) population stability model.
To investigate the complex internal dynamics, including periodicity and chaos, within the Sheperd model.
To consider potential applications of the model in psychophysiological contexts.

Main Methods:

Analysis of the mathematical structure of Sheperd's (1982) equation.
Examination of the model's dynamic behaviors, identifying phases of periodicity and chaos.
Review of potential extensions and applications to psychophysiological data.

Main Results:

Sheperd's (1982) equation demonstrates complex dynamics, including chaotic and periodic phases.
The model's mathematical properties suggest potential applicability to systems beyond fish population dynamics.
The study briefly touches upon model fitting and comparison with alternative mathematical frameworks.

Conclusions:

Sheperd's (1982) model possesses a richer dynamic behavior than initially recognized.
The model's potential extends to psychophysiological research, warranting further investigation.
Further research is needed on model fitting and comparative analysis for validating broader applications.