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First encounters on Watts-Strogatz networks and Barabási-Albert networks
Zhenhua Yuan1, Yongjin Chen1, Long Gao1
1School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China.
Chaos (Woodbury, N.Y.)
|January 1, 2023
Summary
Prey motion significantly impacts predator-prey encounter times on Barabási-Albert networks but has minimal effect on Watts-Strogatz networks. This study quantifies these differences for various network models and initial conditions.
Area of Science:
- Complex networks analysis
- Statistical physics
- Mathematical modeling
Background:
- Watts-Strogatz networks bridge regular lattices and random graphs.
- Barabási-Albert networks explain scale-free network origins.
- Understanding particle encounters in networks is crucial for various applications.
Purpose of the Study:
- To numerically investigate the mean first-encounter time (MFET) and mean first-passage time (MFPT) for two particles in Watts-Strogatz and Barabási-Albert networks.
- To determine the impact of prey motion on encounter times.
- To identify conditions where prey motion accelerates or decelerates encounters.
Main Methods:
- Numerical simulations of particle movement on Watts-Strogatz and Barabási-Albert networks.
- Calculation of MFET for moving particles and MFPT for fixed prey.
- Analysis of different initial conditions, including random and fixed starting sites.
Main Results:
- On Barabási-Albert networks, MFET is significantly less than MFPT, indicating a large impact of prey motion.
- On Watts-Strogatz networks, MFET is comparable to MFPT, showing a smaller impact of prey motion.
- Conditions for prey motion accelerating or decelerating encounters were identified.
Conclusions:
- Prey mobility has a substantial effect on encounter dynamics in scale-free networks (Barabási-Albert) compared to small-world networks (Watts-Strogatz).
- Network topology critically influences how prey movement affects predator-prey interaction times.
- The findings provide insights into encounter dynamics in different network structures.
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