Related Experiment Video

Updated: Aug 16, 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

Stability of synchronous oscillations in a system of Hodgkin-Huxley neurons with delayed diffusive and pulsed

Enrico Rossoni1, Yonghong Chen, Mingzhou Ding

  • 1Department of Informatics, Sussex University, Brighton BN1 9QH, United Kingdom. e.rossoni@sussex.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed

We study the synchronization dynamics for a system of two Hodgkin-Huxley (HH) neurons coupled diffusively or through pulselike interactions. By calculating the maximum transverse Lyapunov exponent, we found that, with diffusive coupling, there are three regions in the parameter space, corresponding to qualitatively distinct behaviors of the coupled dynamics. In particular, the two neurons can synchronize in two regions and desynchronize in the third. When excitatory and inhibitory pulse coupling is considered, we found that synchronized dynamics becomes more difficult to achieve in the sense that the parameter regions where the synchronous state is stable are smaller. Numerical simulations of the coupled system are presented to validate these results. The stability of a network of coupled HH neurons is then analyzed and the stability regions in the parameter space are exactly obtained.

More Related Videos

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice07:33

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice

Published on: June 29, 2018

Generation of Local CA1 γ Oscillations by Tetanic Stimulation08:02

Generation of Local CA1 γ Oscillations by Tetanic Stimulation

Published on: August 14, 2015

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.
Propagation of Action Potentials01:23

Propagation of Action Potentials

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...
Damped Oscillations01:07

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...
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...
Types of Damping01:20

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...