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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.18400 |
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| _version_ | 1866916337153998848 |
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| author | Grover, Piyush Huo, Mandy |
| author_facet | Grover, Piyush Huo, Mandy |
| contents | The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative motile agents with inertial dynamics and finite-range interactions, where each agent is minimizing a biologically inspired cost function. By analyzing the associated coupled forward-backward in time system of nonlinear Fokker-Planck and Hamilton-Jacobi-Bellman equations, we obtain conditions for closed-loop linear stability of the spatially homogeneous MFG equilibrium that corresponds to an ordered state with non-zero mean speed. Using a combination of analysis and numerical simulations, we show that when energetic cost of control is reduced below a critical value, this equilibrium loses stability, and the system transitions to a travelling wave solution. Our work provides a game-theoretic perspective to the problem of collective motion in non-equilibrium biological and bio-inspired systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18400 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase transition in a kinetic mean-field game model of inertial self-propelled agents Grover, Piyush Huo, Mandy Optimization and Control Systems and Control Analysis of PDEs Dynamical Systems Adaptation and Self-Organizing Systems 35Q89, 37L15, 91A16, 93E20, 49L12 The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative motile agents with inertial dynamics and finite-range interactions, where each agent is minimizing a biologically inspired cost function. By analyzing the associated coupled forward-backward in time system of nonlinear Fokker-Planck and Hamilton-Jacobi-Bellman equations, we obtain conditions for closed-loop linear stability of the spatially homogeneous MFG equilibrium that corresponds to an ordered state with non-zero mean speed. Using a combination of analysis and numerical simulations, we show that when energetic cost of control is reduced below a critical value, this equilibrium loses stability, and the system transitions to a travelling wave solution. Our work provides a game-theoretic perspective to the problem of collective motion in non-equilibrium biological and bio-inspired systems. |
| title | Phase transition in a kinetic mean-field game model of inertial self-propelled agents |
| topic | Optimization and Control Systems and Control Analysis of PDEs Dynamical Systems Adaptation and Self-Organizing Systems 35Q89, 37L15, 91A16, 93E20, 49L12 |
| url | https://arxiv.org/abs/2407.18400 |