Conservation laws and asymptotic behavior of a model of social dynamics

Bertotti, Maria Letizia; Delitala, Marcello Edoardo

doi:10.1016/j.nonrwa.2006.09.012

Cited by 57 publications

(37 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the contrary, they seem to be used more and more to investigate various problems in ecology and medicine. Moreover, in the last few years these models have been applied to new research areas, such as social dynamics (Bertotti and Delitala 2008), economy (Marsan et al 2008) or human psychology (Carbonaro and Giordano 2005). Recently, Bellomo and Delitala (2008), Bellomo and Forni (2008) suggested that these kinetic models could be the start of a biological mathematical theory for complex systems.…”

Section: Directions For Future Researchmentioning

confidence: 99%

Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review

Eftimie

2011

J. Math. Biol.

View full text Add to dashboard Cite

We briefly review hyperbolic and kinetic models for self-organized biological aggregations and traffic-like movement. We begin with the simplest models described by an advection-reaction equation in one spatial dimension. We then increase the complexity of models in steps. To this end, we begin investigating local hyperbolic systems of conservation laws with constant velocity. Next, we proceed to investigate local hyperbolic systems with density-dependent speed, systems that consider population dynamics (i.e., birth and death processes), and nonlocal hyperbolic systems. We conclude by discussing kinetic models in two spatial dimensions and their limiting hyperbolic models. This structural approach allows us to discuss the complexity of the biological problems investigated, and the necessity for deriving complex mathematical models that would explain the observed spatial and spatiotemporal group patterns.

show abstract

Section: Directions For Future Researchmentioning

confidence: 99%

Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review

Eftimie

2011

J. Math. Biol.

View full text Add to dashboard Cite

show abstract

“…It is quite clear that the first Helbing model is a discrete velocity model. Note that this kind of model have been used later on to study opinion dynamics phenomena (for example, [6][7][8][9]). However, in the absence of spatial phenomena, their structure more remembers a dynamical system than a kinetic model.…”

Section: Basic Models Towards Continuous Modelsmentioning

confidence: 99%

Modelling opinion formation by means of kinetic equations

Boudin¹,

Salvarani²

2010

Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences

View full text Add to dashboard Cite

In this chapter, we review some mechanisms of opinion dynamics that can be modelled by kinetic equations. Beside the sociological phenomenon of compromise, naturally linked to collisional operators of Boltzmann kind, many other aspects, already mentioned in the sociophysical literature or no, can enter in this framework. While describing some contributions appeared in the literature, we enlighten some mathematical tools of kinetic theory that can be useful in the context of sociophysics

show abstract

“…Specifically, we mean actions addressed to controlling the system, for instance therapeutical actions in the case of biological systems [4], actions devoted to optimizing the flow conditions in the case of traffic flow models [8,9], and actions devoted to controlling economic systems [3]. Consider the specific actions expressed by the following terms: k (t) cause a proliferation or destruction in the state u h of the test particle.…”

Section: Mathematical Framework For Open Systemsmentioning

confidence: 99%

“…Paper [1] deals with a kinetic methodological approach where a class of evolution equations are proposed for modelling large systems of interacting individuals such that the microscopic state is a discrete variable; see also [2,3]. The aim for analyzing such systems is induced by modelling requirements rather than by the intention of reducing computational complexity.…”

Section: Introductionmentioning

confidence: 99%

From the discrete kinetic theory to modelling open systems of active particles

Brazzoli

2008

Applied Mathematics Letters

View full text Add to dashboard Cite

This work deals with a methodological development of the kinetic theory for open systems of active particles with discrete states. It essentially refers to the derivation of mathematical tools which provide the guidelines for modelling open systems in different fields of applied sciences. After a description of closed systems, mathematical frameworks suitable for depicting the evolution of open systems are proposed. Finally, some research perspectives towards modelling are outlined.

show abstract

Conservation laws and asymptotic behavior of a model of social dynamics

Cited by 57 publications

References 13 publications

Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review

Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review

Modelling opinion formation by means of kinetic equations

From the discrete kinetic theory to modelling open systems of active particles

Contact Info

Product

Resources

About