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Impact of anticipation in dynamical systems
P Gerlee1, K Tunstrøm2, T Lundh1
1Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 412 96 Göteborg, Sweden.
Physical Review. E
|January 20, 2018
Summary
Anticipation in particle systems, by predicting future states, can lead to organized hexagonal clusters and energy dissipation. This predictive behavior influences collective dynamics and pattern formation.
Area of Science:
- Physics
- Complex Systems
- Computational Science
Background:
- Many biological systems exhibit predictive capabilities influencing decision-making.
- Understanding predictive mechanisms in simpler physical systems can offer insights into collective behavior.
Purpose of the Study:
- To investigate the effects of anticipation on interacting particles.
- To model how predicting future states impacts particle dynamics and emergent patterns.
Main Methods:
- Simulating particles interacting via a pairwise potential.
- Incorporating anticipation by linear extrapolation of particle positions at a future time τ.
- Analyzing system dynamics, energy, and angular momentum.
Main Results:
- Intermediate anticipation times (τ) induce the formation of rotating hexagonal clusters.
- Anticipation leads to energy dissipation, with kinetic energy decaying as 1/t.
- Angular momentum is not conserved, allowing initial asymmetries to drive rotation.
Conclusions:
- Anticipation can be a fundamental mechanism for pattern formation in collective systems.
- Predictive capabilities can stabilize system dynamics and lead to ordered structures.
- This model provides a minimal framework for understanding anticipation in physical interactions.
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