Related Experiment Video
Updated: Feb 22, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
9.1K
Sustained dynamics of a weakly excitable system with nonlocal interactions
Yasuaki Kobayashi1, Hiroyuki Kitahata2, Masaharu Nagayama3,4
1Center for Simulation Sciences, Ochanomizu University, Tokyo 112-8620, Japan.
Physical Review. E
|September 28, 2017
Summary
This study reveals three distinct sustained dynamics in weakly excitable systems with nonlocal interactions. These dynamics arise from interactions between elementary oscillatory cycles formed by wave propagation.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Computational Physics
Background:
- Weakly excitable systems exhibit limited wave propagation.
- Understanding emergent dynamics in spatially extended systems is crucial.
- Nonlocal interactions can significantly alter system behavior.
Purpose of the Study:
- To investigate emergent dynamics in a 2D weakly excitable system.
- To model wave propagation and oscillatory behavior using a cellular automaton.
- To analyze the role of nonlocal interactions in creating sustained dynamics.
Main Methods:
- Development of a 2D cellular automaton model for a weakly excitable system.
- Incorporation of nonlocal spatial interactions into the model.
- Analysis of wave propagation, oscillatory cycles, and regime transitions.
Main Results:
- Emergence of three distinct types of sustained dynamics.
- Identification of elementary oscillatory cycles formed by local wave propagation and nonlocal activation.
- Explanation of transitions between oscillation regimes based on cycle interactions.
- Derivation of analytical expressions for oscillation probability near onset.
Conclusions:
- Nonlocal interactions are key to generating complex sustained dynamics in weakly excitable systems.
- The interplay of elementary oscillatory cycles governs system behavior.
- The model provides a framework for understanding emergent oscillations in extended systems.
Related Concept Videos
01:07Damped Oscillations
7.4K
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...
Although friction and other non-conservative...
7.4K
01:16Non-equilibrium in the Cell
5.5K
An important concept in studying metabolism and energy is that of chemical equilibrium. Most chemical reactions are reversible. They can proceed in both directions, releasing energy into their environment in one direction, and absorbing it from the environment in the other direction. The same is true for the chemical reactions involved in cell metabolism, such as the breaking down and building up of proteins into and from individual amino acids, respectively. Reactants within a closed system...
5.5K
01:20Types of Damping
7.9K
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...
7.9K
01:24BIBO stability of continuous and discrete -time systems
962
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....
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....
962
01:18Second Order systems II
433
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
433
01:04Oscillations about an Equilibrium Position
7.1K
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...
7.1K