Related Experiment Video
Updated: Aug 6, 2026
06:44
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Oscillatory evolutionarily stable state and limit cycle in replicator dynamics
Suman Chakraborty1, Vikash Kumar Dubey2, Vaibhav Madhok1
1Indian Institute of Technology Madras, Department of Physics, Chennai 600036, India.
Physical Review. E
|July 24, 2026
Summary
This study introduces the oscillatory evolutionarily stable state (OESS), a novel concept in evolutionary game theory. OESS represents a stable limit cycle, expanding our understanding of population dynamics beyond fixed points.
Area of Science:
- Evolutionary Game Theory
- Mathematical Biology
- Population Dynamics
Background:
- The evolutionarily stable state (ESS) is a fundamental concept in evolutionary game theory, analogous to Nash equilibrium.
- ESS describes a population strategy resistant to invasion by rare mutant strategies.
- Replicator dynamics model frequency-dependent selection and survival of the fittest over time.
Purpose of the Study:
- To characterize the evolutionary game-theoretic nature of limit cycles.
- To introduce and define the concept of an oscillatory ESS (OESS).
- To establish the conditions for the existence and location of OESSs.
Main Methods:
- Analysis of replicator dynamics in evolutionary game theory.
- Mathematical definition and proof of the oscillatory ESS (OESS).
- Determination of phase-space conditions for OESS existence.
Main Results:
- An ESS corresponds to a stable fixed point in replicator dynamics.
- Limit cycles in evolutionary game theory are characterized as oscillatory ESS (OESS).
- Conditions for the existence and phase-space locations of OESSs are determined.
Conclusions:
- The study fills a gap in evolutionary game theory by defining OESS.
- OESS provides a framework for understanding cyclical population dynamics.
- This work extends the ESS concept to dynamic, oscillating states.
More Related Videos
Related Concept Videos
01:04Oscillations 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...
01:19Limits with Oscillating Discontinuities
An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the most...
01:19Cyclic Processes And Isolated Systems
A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each path...
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each path...
01:23Stability of Equilibrium Configuration
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
01:07Damped 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...
Although friction and other non-conservative...
01:24BIBO 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.
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.