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Updated: Sep 4, 2025
08:19
Asymmetric Walkway: A Novel Behavioral Assay for Studying Asymmetric Locomotion
Published on: January 15, 2016
8.9K
Random walks with asymmetric time delays.
Kamil Łopuszański1, Jacek Miękisz2
1Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, ulica Banacha 2, 02-097 Warsaw, Poland.
Physical Review. E
|July 20, 2022
Summary
Time delays in random walks can unexpectedly alter walker behavior, influencing population dynamics in evolutionary games. Asymmetric delays combined with specific fitness functions reveal novel equilibrium structures.
Area of Science:
- Complex Systems
- Evolutionary Game Theory
- Stochastic Processes
Background:
- Dynamical systems with time delays typically exhibit oscillations.
- Random walks are fundamental models for stochastic processes.
Purpose of the Study:
- To investigate the impact of asymmetric time delays on random walks.
- To explore the relationship between time delays, fitness functions, and population dynamics.
Main Methods:
- Modeling random walks with asymmetric time delays.
- Analyzing the dependence of walker position on time delays and fitness functions.
- Connecting random walker position to strategy frequencies in discrete replicator dynamics.
Main Results:
- Observed a dependence of the mean walker position on time delays, contrary to typical expectations.
- Found that the effect of time delays is reversed by symmetric shifts in fitness functions.
- Demonstrated a joint effect of stochasticity and time delays on system behavior.
Conclusions:
- Asymmetric time delays can lead to non-oscillatory behaviors in random walks.
- The equilibrium structure of populations in evolutionary games is sensitive to both time delays and the specifics of fitness functions.
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