Related Experiment Video
Updated: Jun 8, 2026
08:44
Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism
Published on: October 17, 2025
Wave propagation in a FitzHugh-Nagumo-type model with modified excitability
1Department of Chemistry, Brandeis University, MS 015, Waltham, MA 02454, USA. zemskov@brandeis.edu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
This study analyzes a modified neuronal excitability model, finding unique wave behaviors in inhibitor species and confirming a key bifurcation persists under altered parameters.
Area of Science:
- Computational neuroscience
- Mathematical biology
- Nonlinear dynamics
Background:
- The FitzHugh-Nagumo (FHN) model is a foundational tool for studying neuronal excitability.
- Understanding wave propagation in neuronal networks is crucial for deciphering brain function.
- Previous models often simplify reaction kinetics, potentially limiting biological realism.
Purpose of the Study:
- To investigate a generalized FitzHugh-Nagumo (FHN) model incorporating modified excitability from the Morris-Lecar equations.
- To analytically derive and characterize traveling wave solutions.
- To explore the existence, stability, and bifurcations of these waves.
Main Methods:
- Utilized a piecewise linear approximation for activator and inhibitor reaction terms.
- Obtained exact analytic solutions for traveling waves.
- Analyzed wave existence and stability conditions.
- Investigated bifurcation phenomena by varying model parameters.
Main Results:
- Identified distinct wave forms (fronts and pulses) for the inhibitor species.
- Confirmed the activator wave maintains a standard kink (front) shape.
- Demonstrated that the nonequilibrium Ising-Bloch bifurcation for wave speed persists.
- Showed this bifurcation remains when inhibitor nonlinearity strength is the control parameter.
Conclusions:
- The generalized FHN model with modified excitability exhibits rich wave dynamics.
- Analytic solutions provide precise insights into neuronal wave propagation.
- The persistence of the Ising-Bloch bifurcation highlights the robustness of this dynamic phenomenon in neuronal models.
More Related Videos
Related Concept Videos
01:23Propagation 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...
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...
01:28Debye–Huckel–Onsager Conductance Equation
The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
01:20Types 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...
01:29Pharmacodynamic Models: Direct Effect Model and Indirect Response Model
Pharmacodynamic models are essential tools in understanding the relationship between drug concentrations and their effects on biological systems. By characterizing the dynamics of drug action, these models guide dose selection, optimize therapeutic efficacy, and inform the development of new drugs. Two major classes of pharmacodynamic models include direct effect and indirect response models.Direct Effect ModelsDirect effect models describe the immediate relationship between drug concentration...
01:27Pharmacodynamic Models: Overview
Pharmacodynamic (PD) responses describe the interaction between a drug and its biological target, culminating in a physiological effect. These responses can be classified into different types: continuous variables, such as blood glucose levels; categorical outcomes, like survival rates; and time-to-event metrics, such as disease progression. Understanding and modeling PD responses are critical for optimizing drug efficacy and safety.PD models describe the relationship between drug concentration...
01:26Transmission-Line Differential Equations
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...