Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Action Potential: Phases of Stimulation01:28

Action Potential: Phases of Stimulation

The action potential is a complex electrical event that occurs in excitable cells, such as neurons and muscle cells. It consists of several distinct phases, each with specific characteristics.
Resting Phase:
In this phase, the cell's membrane is at its resting potential, typically around -70 millivolts (mV) for neurons. Inside the cell, there is a higher concentration of potassium ions (K+) and a lower concentration of sodium ions (Na+). Voltage-gated sodium channels are closed, and...
Forced Oscillations01:06

Forced Oscillations

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.
Neural Circuits01:25

Neural Circuits

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...
The Role of Ion Channels in Neuronal Computation01:19

The Role of Ion Channels in Neuronal Computation

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.
Phase Transitions02:31

Phase Transitions

Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to occupy...
Phase Transitions01:21

Phase Transitions

A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...

You might also read

Related Articles

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

Sort by
Same author

Resource diversity and supply drive colonization resistance.

PLoS computational biology·2025
Same author

The Kuramoto model on a sphere: Explaining its low-dimensional dynamics with group theory and hyperbolic geometry.

Chaos (Woodbury, N.Y.)·2021
Same author

Dynamics of the Kuramoto-Sakaguchi oscillator network with asymmetric order parameter.

Chaos (Woodbury, N.Y.)·2019
Same author

Cluster synchronization in networks of identical oscillators with α-function pulse coupling.

Physical review. E·2017
Same author

Classification of attractors for systems of identical coupled Kuramoto oscillators.

Chaos (Woodbury, N.Y.)·2014
Same author

Structure of long-term average frequencies for Kuramoto oscillator systems.

Physical review letters·2012
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

Related Experiment Video

Updated: Jun 23, 2026

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
08:08

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

Published on: June 24, 2015

Dynamical phase transitions in periodically driven model neurons.

Jan R Engelbrecht1, Renato Mirollo

  • 1Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 28, 2009
PubMed
Summary
This summary is machine-generated.

Transitions in neuron firing states arise from bifurcations. Discontinuous bifurcations show unique phase transitions, simplifying complex neuron dynamics to a 1D map for broader applications.

More Related Videos

Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses
08:34

Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses

Published on: May 9, 2021

Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism
08:44

Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism

Published on: October 17, 2025

Related Experiment Videos

Last Updated: Jun 23, 2026

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
08:08

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

Published on: June 24, 2015

Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses
08:34

Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses

Published on: May 9, 2021

Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism
08:44

Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism

Published on: October 17, 2025

Area of Science:

  • Computational Neuroscience
  • Dynamical Systems Theory
  • Mathematical Biology

Background:

  • Integrate-and-fire neuron models are fundamental to neuroscience.
  • Periodic stimuli induce complex dynamical state transitions.
  • Bifurcations of return maps characterize these transitions.

Purpose of the Study:

  • To analyze scaling laws of bifurcations in neuron models.
  • To characterize phase transitions in discontinuous bifurcations.
  • To demonstrate model-independent reduction of complex neural dynamics.

Main Methods:

  • Analysis of tangent and discontinuous bifurcations.
  • Study of characteristic scaling laws.
  • Reduction of a 6D gating variable model to a 1D return map.

Main Results:

  • Discontinuous bifurcations exhibit intermediate phase transitions.
  • A 6D model's dynamics were governed by a 1D return map.
  • Model-independent analysis revealed universal properties.

Conclusions:

  • Neuron state transitions are governed by bifurcations.
  • Discontinuous bifurcations represent a novel class of phase transitions.
  • The 1D return map reduction is applicable to real neurons under periodic current clamp.