Continuum Limit of Self-Driven Particles With Orientation Interaction

Degond, Pierre; Motsch, Sébastien

doi:10.1142/s0218202508003005

Cited by 332 publications

(640 citation statements)

References 34 publications

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“…Several attempts to derive continuum models from the CVA model are also reported in the literature [34,44,45]. In [21,22], a derivation of a continuum model from a kinetic version of the CVA model is proposed. However, few Individual Based Models for fish have been validated against experimental data with a comparable care as in [27] for the PTW process.…”

Section: Introductionmentioning

confidence: 99%

Large Scale Dynamics of the Persistent Turning Walker Model of Fish Behavior

2008

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This paper considers a new model of individual displacement, based on fish motion, the so-called Persistent Turning Walker (PTW) model, which involves an Ornstein-Uhlenbeck process on the curvature of the particle trajectory. The goal is to show that its large time and space scale dynamics is of diffusive type, and to provide an analytic expression of the diffusion coefficient. Two methods are investigated. In the first one, we compute the large time asymptotics of the variance of the individual stochastic trajectories. The second method is based on a diffusion approximation of the kinetic formulation of these stochastic trajectories. The kinetic model is a Fokker-Planck type equation posed in an extended phase-space involving the curvature among the kinetic variables. We show that both methods lead to the same value of the diffusion constant. We present some numerical simulations to illustrate the theoretical results.Acknowledgements: The authors wish to thank Guy Théraulaz and Jacques Gautrais of the 'Centre de Recherches sur la Cognition Animale' in Toulouse, for introducing them to the model and for stimulating discussions.

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Section: Introductionmentioning

confidence: 99%

Large Scale Dynamics of the Persistent Turning Walker Model of Fish Behavior

2008

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“…In several recent works additional variables have been introduced quantifying relevant indicators for the spreading of opinions [9,10,31,54,58,91]. In this class of models the opinion dynamics depends on an additional parameter, continuous or discrete, which influences the binary exchanges.…”

Section: Multivariate Modelsmentioning

confidence: 99%

Recent Advances in Opinion Modeling: Control and Social Influence

Albi

Pareschi

Toscani

et al. 2017

Modeling and Simulation in Science, Engineering and Technology

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We survey some recent developments on the mathematical modeling of opinion dynamics. After an introduction on opinion modeling through interacting multi-agent systems described by partial differential equations of kinetic type, we focus our attention on two major advancements: optimal control of opinion formation and influence of additional social aspects, like conviction and number of connections in social networks, which modify the agents' role in the opinion exchange process. PreliminariesWe introduce some of the essential literature on the opinion formation, by emphasizing the role of the kinetic description. New problems recently treated in the scientific community are outlined. Then, the mathematical description of the core ideas of kinetic models for opinion formation are presented in details.

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“…[15,16]) and better understand phase transitions, i.e. critical values of certain parameters needed to successfully form flocks [17][18][19].…”

Section: Spatial Pattern Formation By Consensus and Herdingmentioning

confidence: 99%

Partial differential equation models in the socio-economic sciences

Burger

Caffarelli

Markowich

2014

Phil. Trans. R. Soc. A.

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Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences. The application of PDEs in the latter is a promising field, but widely quite open and leading to a variety of novel mathematical challenges. In this introductory article of the Theme Issue, we will provide an overview of the field and its recent boosting topics. Moreover, we will put the contributions to the Theme Issue in an appropriate perspective.

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Continuum Limit of Self-Driven Particles With Orientation Interaction

Cited by 332 publications

References 34 publications

Large Scale Dynamics of the Persistent Turning Walker Model of Fish Behavior

Large Scale Dynamics of the Persistent Turning Walker Model of Fish Behavior

Recent Advances in Opinion Modeling: Control and Social Influence

Partial differential equation models in the socio-economic sciences

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