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Related Concept Videos

Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

3.0K
An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
3.0K
RLC Circuit as a Damped Oscillator01:30

RLC Circuit as a Damped Oscillator

2.0K
An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
2.0K
Design Example: Underdamped Parallel RLC Circuit01:17

Design Example: Underdamped Parallel RLC Circuit

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Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...
592
Second-Order Circuits01:17

Second-Order Circuits

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Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
3.2K
LC Circuits01:21

LC Circuits

3.2K
An LC circuit consists of an inductor and a capacitor, either in series or parallel. Consider a charged capacitor connected with an inductor in series. Before the switch is closed, all the energy of the circuit is stored in the electric field of the capacitor. When the switch is closed, the capacitor begins to discharge, producing a current in the circuit. The current, in turn, creates a magnetic field in the inductor. Because of the induced emf in the inductor, the current cannot change...
3.2K
Forced Oscillations01:06

Forced Oscillations

7.5K
When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
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Related Experiment Video

Updated: Jan 4, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Hyperchaos in Wilson-Cowan oscillator circuits.

Hugh R Wilson1

  • 1Centre for Vision Research, York University, Toronto, Ontario, Canada.

Journal of Neurophysiology
|October 31, 2019
PubMed
Summary

Coupled Wilson-Cowan equations generate hyperchaos, a complex neural response. This unpredictability in neural networks may explain variations in human behaviors and cognitive functions.

Area of Science:

  • Computational neuroscience
  • Dynamical systems theory
  • Neural network modeling

Background:

  • The Wilson-Cowan equations model neural population activity, known to produce limit cycles and chaos in coupled systems.
  • Previous work demonstrated chaos in two coupled Wilson-Cowan oscillators, particularly with specific inhibitory-excitatory coupling.

Purpose of the Study:

  • To investigate the emergence of hyperchaos in larger networks of coupled Wilson-Cowan oscillators.
  • To explore the relationship between network complexity and the degree of hyperchaos.
  • To connect these findings to the unpredictability observed in human behaviors.

Main Methods:

  • Simulating chains, grids, and sparse networks of Wilson-Cowan oscillators.
  • Analyzing the dynamics of these networks, focusing on the number of positive Lyapunov exponents to quantify hyperchaos.
Keywords:
Wilson–Cowanhyperchaosneural chaosneural simulation

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Last Updated: Jan 4, 2026

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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  • Correlating network size and structure with the observed complexity.

    • Main Results:

    • Networks of Wilson-Cowan oscillators generate hyperchaos.
    • The complexity of hyperchaos, measured by the number of positive Lyapunov exponents, increases linearly with the number of oscillators.
    • This linear increase in complexity suggests a scalable mechanism for generating unpredictable neural dynamics.

    Conclusions:

    • Coupled Wilson-Cowan equations can generate hyperchaos in complex network structures.
    • The linear scaling of hyperchaos with network size provides a potential neural basis for the unpredictability in human behaviors.
    • These findings have implications for understanding aging, brain injuries, autism, intelligence, and creativity.