Related Experiment Video
Updated: Apr 18, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
9.1K
Classification of wave regimes in excitable systems with linear cross diffusion.
1Institute of Theoretical and Experimental Biophysics, Pushchino, Moscow Region, 142290, Russia.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 24, 2015
Summary
This study explores wave behaviors in excitable systems, detailing fixed-shape, envelope, and multienvelope waves. It examines their interactions and boundary reflections, including quasisoliton properties in 1D and 2D.
Area of Science:
- Nonlinear dynamics
- Mathematical modeling
- Physical chemistry
Background:
- Excitable systems exhibit complex wave phenomena.
- Cross-diffusion significantly impacts wave dynamics.
- Understanding wave regimes is crucial for various scientific fields.
Purpose of the Study:
- To investigate principal properties of diverse wave regimes in excitable systems.
- To analyze the influence of linear cross-diffusion on wave behavior.
- To characterize fixed-shape, envelope, and multienvelope waves, including intermediate regimes.
Main Methods:
- Numerical simulations of two selected excitable systems in one spatial dimension.
- Analysis of wave properties at varying parameter values.
- Examination of wave interactions, boundary reflections, and quasisoliton behavior.
Main Results:
- Identified and characterized fixed-shape, envelope, multienvelope, and intermediate wave regimes.
- Demonstrated that most regimes exhibit or lack quasisoliton properties (boundary reflection, mutual penetration).
- Presented examples of envelope quasisoliton behavior in two spatial dimensions.
Conclusions:
- Wave dynamics in excitable systems are highly dependent on system parameters and cross-diffusion.
- Quasisoliton properties significantly influence wave interactions and system behavior.
- The study provides insights into complex wave phenomena in both one and two spatial dimensions.
More Related Videos
Related Concept Videos
01:31Classification of Systems-II
584
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
584
01:26Classification of Systems-I
709
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
709
01:26Linear Approximation in Frequency Domain
457
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
457
01:07Propagation of Waves
3.4K
When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
3.4K
01:23Linear time-invariant Systems
1.1K
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
1.1K
01:27Traveling Waves: Lossless Lines
541
The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx and a shunt capacitance CΔx.
541