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Hyperbolic and kinetic models for self-organized biological aggregations and movement

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Hyperbolic and kinetic models for self-organized biological aggregations and movement : a brief review. / Eftimie, R.

In: Journal of Mathematical Biology, Vol. 65, No. 1, 2012, p. 35-75.

Research output: Contribution to journalScientific review

Harvard

Eftimie, R 2012, 'Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review' Journal of Mathematical Biology, vol 65, no. 1, pp. 35-75., 10.1007/s00285-011-0452-2

APA

Eftimie, R. (2012). Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review. Journal of Mathematical Biology, 65(1), 35-75. 10.1007/s00285-011-0452-2

Vancouver

Eftimie R. Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review. Journal of Mathematical Biology. 2012;65(1):35-75. Available from: 10.1007/s00285-011-0452-2

Author

Eftimie, R. / Hyperbolic and kinetic models for self-organized biological aggregations and movement : a brief review.

In: Journal of Mathematical Biology, Vol. 65, No. 1, 2012, p. 35-75.

Research output: Contribution to journalScientific review

Bibtex - Download

@article{da979995e8a24e2ca32bab5345c5597c,
title = "Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review",
author = "R. Eftimie",
year = "2012",
doi = "10.1007/s00285-011-0452-2",
volume = "65",
number = "1",
pages = "35--75",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Hyperbolic and kinetic models for self-organized biological aggregations and movement

T2 - a brief review

A1 - Eftimie,R.

AU - Eftimie,R.

PY - 2012

Y1 - 2012

N2 - 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. © 2011 Springer-Verlag.

AB - 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. © 2011 Springer-Verlag.

UR - http://www.scopus.com/inward/record.url?scp=79959627467&partnerID=8YFLogxK

U2 - 10.1007/s00285-011-0452-2

DO - 10.1007/s00285-011-0452-2

M1 - Scientific review

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 1

VL - 65

SP - 35

EP - 75

ER -

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