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Neural Circuits01:25

Neural Circuits

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Neural circuits and neuronal pools are two of the main structures found in the nervous system. Neural circuits are networks of neurons that work together to carry out a specific task or process. They consist of interconnected neurons and glial cells, which provide structural and metabolic support.
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
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The Role of Ion Channels in Neuronal Computation01:19

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A postsynaptic neuron usually receives numerous impulses from several other presynaptic neurons. The axon hillock of the postsynaptic neuron integrates all these signals and determines the likelihood of firing an action potential.
Sometimes a single EPSP is strong enough to induce an action potential in the postsynaptic neuron. However, multiple presynaptic inputs must often create EPSPs around the same time for the postsynaptic neuron to be sufficiently depolarized to fire an action potential....
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Neuronal Communication01:28

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Neurons, the fundamental units of the brain and nervous system, communicate through complex electrochemical signals that underpin all cognitive and bodily functions. This communication is primarily facilitated by a process involving the generation and propagation of an action potential along the axon of the neuron. When the internal electrical charge of a neuron surpasses a certain threshold, an action potential is triggered. This rapid change in voltage travels swiftly along the axon to the...
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Propagation of Action Potentials01:23

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The propagation of an action potential refers to the process by which a nerve impulse, or "action potential," travels along a neuron.
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
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Electrical Synapses01:28

Electrical Synapses

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Electrical synapses found in all nervous systems play important and unique roles. In these synapses, the presynaptic and postsynaptic membranes are very close together (3.5 nm) and are actually physically connected by channel proteins forming gap junctions.
Gap junctions allow the current to pass directly from one cell to the next. In contrast, in the chemical synapse, the neurotransmitters carry the information through the synaptic cleft from one neuron to the next. They consist of two...
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Neurons: The Axon01:21

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Axons are long, cytoplasmic processes of nerve cells capable of propagating electrical impulses known as action potentials. The cytoplasm or axoplasm of an axon contains neurofibrils, neurotubules, small vesicles, lysosomes, mitochondria, and various enzymes, all encased within the axolemma, the plasma membrane of the axon.
The axon attaches to the cell body at a cone-shaped elevation called the axon hillock. The initial part of the axon, closest to the hillock, is known as the initial segment....
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Related Experiment Video

Updated: Aug 19, 2025

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
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Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond

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Cupolets in a chaotic neuron model.

John E Parker1, Kevin M Short1

  • 1Integrated Applied Mathematics Program, Department of Mathematics and Statistics, University of New Hampshire, Durham, New Hampshire 03824, USA.

Chaos (Woodbury, N.Y.)
|December 1, 2022
PubMed
Summary
This summary is machine-generated.

Researchers discovered cupolets (chaotic, unstable, periodic, orbit-lets) in the Hindmarsh-Rose neural model. These unstable orbits were stabilized using a binary control sequence, offering new insights into neural dynamics.

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Area of Science:

  • Computational Neuroscience
  • Nonlinear Dynamics
  • Chaos Theory

Background:

  • The Hindmarsh-Rose model is a classic mathematical model of neuronal bursting.
  • Unstable periodic orbits are fundamental to understanding complex dynamics in nonlinear systems.
  • Cupolets, a specific type of stabilized unstable periodic orbit, have been previously observed in other chaotic systems.

Purpose of the Study:

  • To report the first discovery of cupolets within a chaotic Hindmarsh-Rose neural model.
  • To investigate the stabilization of unstable periodic orbits in a neural model using a novel control scheme.
  • To explore the characteristics and generation of cupolets in this specific neural context.

Main Methods:

  • Numerical simulations of the Hindmarsh-Rose model were performed.
  • A bifurcation diagram was used to identify regions of periodic and chaotic dynamics, with external input current (I) as the bifurcation parameter.
  • A control scheme was applied when the system's trajectory intersected predefined control planes, utilizing a binary control sequence (0 for microcontrol, 1 for macrocontrol).

Main Results:

  • The study successfully identified and generated numerous cupolets within the chaotic parameter space of the Hindmarsh-Rose model.
  • The applied binary control sequence effectively stabilized previously unstable periodic orbits.
  • Differences in cupolet characteristics were noted compared to those found in the double scroll system.

Conclusions:

  • The findings demonstrate the existence and controllability of cupolets in a Hindmarsh-Rose neural model.
  • This research expands the understanding of stabilized unstable periodic orbits in neural modeling.
  • The results suggest potential implications for understanding and manipulating biological neuron behavior.