scholarly journals The mean field kinetic equation for interacting particle systems with non‐Lipschitz force

2019 ◽  
Vol 43 (4) ◽  
pp. 1901-1914
Author(s):  
Qitao Yin ◽  
Li Chen ◽  
Simone Göttlich
Keyword(s):  
Kinetic Equation ◽  
Interacting Particle Systems ◽  
Mean Field ◽  
Particle Systems ◽  
Interacting Particle ◽  
The Mean

scholarly journals Instantaneous control of interacting particle systems in the mean-field limit

2020 ◽  
Vol 405 ◽  
pp. 109181 ◽  
Author(s):  
Martin Burger ◽  
René Pinnau ◽  
Claudia Totzeck ◽  
Oliver Tse ◽  
Andreas Roth
Keyword(s):  
Interacting Particle Systems ◽  
Mean Field ◽  
Particle Systems ◽  
Field Limit ◽  
Mean Field Limit ◽  
Interacting Particle ◽  
The Mean ◽  
Instantaneous Control

Game Theory Cancer Models of Cancer Cell-Stromal Cell Dynamics using Interacting Particle Systems

2020 ◽  
Vol 15 (03) ◽  
pp. 171-193
Author(s):  
Yinan Zheng ◽  
Yusha Sun ◽  
Gonzalo Torga ◽  
Kenneth Pienta ◽  
Robert Austin
Keyword(s):  
Game Theory ◽  
Interacting Particle Systems ◽  
Evolutionary Game ◽  
Mean Field ◽  
Theory Model ◽  
Particle Systems ◽  
Cell Dynamics ◽  
Field Approach ◽  
Interacting Particle ◽  
The Mean

We describe an evolutionary game theory model that has been used to predict the population dynamics of interacting cancer and stromal cells. We first consider the mean field case assuming homogeneous and nondiscrete populations. Interacting Particle Systems (IPS) are then presented as a discrete and spatial alternative to the mean field approach. Finally, we discuss cases where IPS gives results different from the mean field approach.

The propagation of chaos of multitype mean field interacting particle systems

1997 ◽  
Vol 34 (2) ◽  
pp. 346-362 ◽  
Author(s):  
Shui Feng
Keyword(s):  
Interacting Particle Systems ◽  
Mean Field ◽  
Technical Difficulty ◽  
Particle Systems ◽  
Self Organization ◽  
Propagation Of Chaos ◽  
Field Interaction ◽  
Interacting Particle

A result for the propagation of chaos is obtained for a class of pure jump particle systems of two species with mean field interaction. This result leads to the corresponding result for particle systems with one species and the argument used is valid for particle systems with more than two species. The model is motivated by the study of the phenomenon of self-organization in biology, chemistry and physics, and the technical difficulty is the unboundedness of the jump rates.

The propagation of chaos of multitype mean field interacting particle systems

1997 ◽  
Vol 34 (02) ◽  
pp. 346-362 ◽  
Author(s):  
Shui Feng
Keyword(s):  
Interacting Particle Systems ◽  
Mean Field ◽  
Technical Difficulty ◽  
Particle Systems ◽  
Self Organization ◽  
Propagation Of Chaos ◽  
Field Interaction ◽  
Interacting Particle

A result for the propagation of chaos is obtained for a class of pure jump particle systems of two species with mean field interaction. This result leads to the corresponding result for particle systems with one species and the argument used is valid for particle systems with more than two species. The model is motivated by the study of the phenomenon of self-organization in biology, chemistry and physics, and the technical difficulty is the unboundedness of the jump rates.

SELF-PROPELLED INTERACTING PARTICLE SYSTEMS WITH ROOSTING FORCE

2010 ◽  
Vol 20 (supp01) ◽  
pp. 1533-1552 ◽  
Author(s):  
JOSÉ A. CARRILLO ◽  
AXEL KLAR ◽  
STEPHAN MARTIN ◽  
SUDARSHAN TIWARI
Keyword(s):  
Stochastic Model ◽  
Collective Behavior ◽  
Food Source ◽  
Interacting Particle Systems ◽  
Particle System ◽  
Mean Field ◽  
Particle Systems ◽  
Interacting Particle System ◽  
Hydrodynamic Equations ◽  
Interacting Particle

We consider a self-propelled interacting particle system for the collective behavior of swarms of animals, and extend it with an attraction term called roosting force, as it has been suggested in Ref. 30. This new force models the tendency of birds to overfly a fixed preferred location, e.g. a nest or a food source. We include roosting to the existing individual-based model and consider the associated mean-field and hydrodynamic equations. The resulting equations are investigated analytically looking at different asymptotic limits of the corresponding stochastic model. In addition to existing patterns like single mills, the inclusion of roosting yields new scenarios of collective behavior, which we study numerically on the microscopic as well as on the hydrodynamic level.

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