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Updated: Jun 19, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Dissipative system with asymmetric interaction and Hopf bifurcation
Masami Yamamoto1, Yasuyuki Nomura, Yuki Sugiyama
1Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Nagoya 464-8601, Japan. yamamoto@phys.cs.is.nagoya-u.ac.jp
Summary
Asymmetric interactions in microscopic systems drive Hopf bifurcations in macroscopic phenomena. This leads to pattern formation, transitioning from uniform motion to complex structures.
Area of Science:
- Physics
- Complex Systems
- Nonlinear Dynamics
Background:
- Dissipative systems with asymmetric interactions often exhibit Hopf bifurcations.
- These bifurcations mark transitions from homogeneous motion to pattern formation.
- Optimal velocity models are frequently associated with these phenomena.
Purpose of the Study:
- To investigate the microscopic origins of Hopf bifurcations in macroscopic dissipative systems.
- To establish a link between microscopic asymmetric interactions and macroscopic pattern formation.
- To analyze the role of the optimal velocity model in this transition.
Main Methods:
- Derivation of a continuum system from an original discrete many-body system.
- Analysis of the continuum system to identify the conditions for Hopf bifurcation.
- Mathematical modeling of asymmetric interactions in microscopic systems.
Main Results:
- The study reveals that microscopic asymmetric interactions are the fundamental cause of Hopf bifurcations.
- A direct relationship is established between the asymmetry at the microscopic level and the emergence of macroscopic patterns.
- The continuum model successfully captures the transition from homogeneous to nontrivial states.
Conclusions:
- Hopf bifurcations in macroscopic dissipative systems are rooted in microscopic asymmetric interactions.
- Understanding these microscopic origins is crucial for predicting and controlling pattern formation.
- The derived continuum system provides a valuable framework for studying such complex phenomena.
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