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Related Concept Videos

BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Separable Differential Equations01:20

Separable Differential Equations

A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
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Second Order systems II01:18

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...
Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Related Experiment Video

Updated: May 31, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

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

Published on: September 23, 2025

Desynchronization bifurcation of coupled nonlinear dynamical systems.

Suman Acharyya1, R E Amritkar

  • 1Theoretical Physics Division, Physical Research Laboratory, Navrangpura, Ahmedabad, Gujarat 380009, India. suman@prl.res.in

Chaos (Woodbury, N.Y.)
|July 5, 2011
PubMed
Summary
This summary is machine-generated.

We analyzed desynchronization bifurcations in coupled Rössler oscillators. After bifurcation, oscillators diverge with square-root dependence, indicating a pitchfork bifurcation of the transverse manifold.

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Last Updated: May 31, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

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

Published on: September 23, 2025

Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Coupled Oscillators

Background:

  • Coupled oscillators exhibit complex dynamics, including synchronization and desynchronization phenomena.
  • Understanding bifurcations in coupled systems is crucial for predicting transitions between different dynamical states.

Purpose of the Study:

  • To analyze the desynchronization bifurcation in coupled Rössler oscillators.
  • To define and utilize system transverse Lyapunov exponents (STLE) to characterize the desynchronized state.
  • To investigate similar phenomena in simpler coupled integrable systems.

Main Methods:

  • Analysis of coupled Rössler oscillators near a desynchronization bifurcation point.
  • Definition and computation of system transverse Lyapunov exponents (STLE).
  • Modeling coupled integrable systems with quadratic and cubic nonlinearities.

Main Results:

  • Desynchronization occurs as a pitchfork bifurcation of the transverse manifold.
  • In the desynchronized state, STLEs exhibit one positive and one negative value.
  • A simple model with quadratic nonlinearity replicates this desynchronization phenomenon.
  • Cubic nonlinearity leads to bifurcation with two negative STLEs.

Conclusions:

  • Desynchronization in coupled Rössler oscillators is characterized by a pitchfork bifurcation.
  • The behavior of STLEs provides insight into the nature of the desynchronized state.
  • The findings are generalizable to other coupled nonlinear systems.