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Related Concept Videos

Toroids01:27

Toroids

A toroid is a closely wound donut-shaped coil constructed using a single conducting wire. In general, it is assumed that a toriod consists of multiple circular loops perpendicular to its axis.
When connected to a supply, the magnetic field generated in the toroid has field lines circular and concentric to its axis. Conventionally, the direction of this magnetic field is expressed using the right-hand rule. If the fingers of the right hand curl in the current direction, the thumb points in the...
Torsion of Noncircular Members01:16

Torsion of Noncircular Members

Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...
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Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
Node Analysis for AC Circuits01:14

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Torque On A Current Loop In A Magnetic Field01:13

Torque On A Current Loop In A Magnetic Field

The most common application of magnetic force on current-carrying wires is in electric motors. These consist of loops of wire, which are placed between the magnets with a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate, thus converting electrical energy to mechanical energy.
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Related Experiment Video

Updated: May 31, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

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Published on: July 19, 2016

An elementary model of torus canards.

G Nicholas Benes1, Anna M Barry, Tasso J Kaper

  • 1Department of Mathematics and Statistics, Center for BioDynamics, Boston University, Boston, Massachusetts 02215, USA.

Chaos (Woodbury, N.Y.)
|July 5, 2011
PubMed
Summary

Torus canards, complex trajectories in fast-slow systems, exhibit unique dynamics. This study reveals how phase dependence in a simple model generates rich torus canard and mixed-mode behaviors, offering insights into neuroscience models.

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Last Updated: May 31, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Area of Science:

  • Dynamical Systems Theory
  • Nonlinear Dynamics
  • Mathematical Neuroscience

Background:

  • Canard orbits are classical phenomena in planar fast-slow systems.
  • Torus canards are higher-dimensional generalizations observed in systems with saddle-node bifurcations of limit cycles.
  • These trajectories exhibit complex behavior, spending extended periods near repelling limit cycles.

Purpose of the Study:

  • To investigate torus canard dynamics in an elementary third-order system.
  • To analyze the influence of broken rotational symmetry and phase dependence on torus canards.
  • To provide insights into torus canards observed in complex neuroscience models.

Main Methods:

  • Analysis of a third-order ordinary differential equation system.
  • Study of a rotated van der Pol type system with a phase-dependent term.
  • Examination of dynamics in fast and slow rotation regimes.

Main Results:

  • In fast rotation, torus canards resemble planar counterparts.
  • Slow rotation with phase dependence leads to rich torus canard dynamics and mixed-mode behaviors.
  • The elementary model successfully replicates key aspects of torus canard phenomena.

Conclusions:

  • Phase dependence is crucial for generating complex torus canard dynamics.
  • The studied third-order system serves as a valuable model for understanding higher-dimensional torus canards.
  • Findings offer a simplified yet insightful perspective on torus canards in neuroscience applications.