Lessons on pattern formation from planet WATOR

Rick Durrett; Simon Asher Levin

doi:10.1006/jtbi.2000.2061

Lessons on pattern formation from planet WATOR

Rick Durrett, Simon Asher Levin

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

It is well known that if reacting species experience unequal diffusion rates, then dynamics that lead to a constant steady state in a 'well-mixed' environment can in a spatial setting lead to interesting patterns. In this paper, we focus on complementary pattern formation mechanisms that operate even when the diffusion rates are equal. In particular, we can say that when the mean-field ODE has an attracting periodic orbit then the stochastic spatial model will have large-scale spatial structures in equilibrium. We explore this mechanism in depth through the dynamics of the simulator WATOR. (C) 2000 Academic Press.

Original language	English (US)
Pages (from-to)	201-214
Number of pages	14
Journal	Journal of Theoretical Biology
Volume	205
Issue number	2
DOIs	https://doi.org/10.1006/jtbi.2000.2061
State	Published - Jul 21 2000

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Biochemistry, Genetics and Molecular Biology(all)
Immunology and Microbiology(all)
Agricultural and Biological Sciences(all)
Applied Mathematics

Access to Document

10.1006/jtbi.2000.2061

Cite this

@article{2565b759ff1944ada0951ed5a5c62156,

title = "Lessons on pattern formation from planet WATOR",

abstract = "It is well known that if reacting species experience unequal diffusion rates, then dynamics that lead to a constant steady state in a 'well-mixed' environment can in a spatial setting lead to interesting patterns. In this paper, we focus on complementary pattern formation mechanisms that operate even when the diffusion rates are equal. In particular, we can say that when the mean-field ODE has an attracting periodic orbit then the stochastic spatial model will have large-scale spatial structures in equilibrium. We explore this mechanism in depth through the dynamics of the simulator WATOR. (C) 2000 Academic Press.",

author = "Rick Durrett and Levin, {Simon Asher}",

note = "Funding Information: Work on this project began in 1991. Semyon Krug-lyak, then an undergraduate at Cornell, but now a postdoc at the University of Southern California, did some of the {"}rst simulations in the Fall of 1992. Later that work was taken over by Linda Buttel who performed the simulations shown. Buttel has been partially supported by the Cornell Theory Center, and by NSF grant BIR-9423339 from the computational biology program. During this period Durrett has been supported by NSF grants from the probability program. Levin was supported by the Sloan Foundation Grant 97-3-5.",

year = "2000",

month = jul,

day = "21",

doi = "10.1006/jtbi.2000.2061",

language = "English (US)",

volume = "205",

pages = "201--214",

journal = "Journal of Theoretical Biology",

issn = "0022-5193",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Lessons on pattern formation from planet WATOR

AU - Durrett, Rick

AU - Levin, Simon Asher

N1 - Funding Information: Work on this project began in 1991. Semyon Krug-lyak, then an undergraduate at Cornell, but now a postdoc at the University of Southern California, did some of the "rst simulations in the Fall of 1992. Later that work was taken over by Linda Buttel who performed the simulations shown. Buttel has been partially supported by the Cornell Theory Center, and by NSF grant BIR-9423339 from the computational biology program. During this period Durrett has been supported by NSF grants from the probability program. Levin was supported by the Sloan Foundation Grant 97-3-5.

PY - 2000/7/21

Y1 - 2000/7/21

N2 - It is well known that if reacting species experience unequal diffusion rates, then dynamics that lead to a constant steady state in a 'well-mixed' environment can in a spatial setting lead to interesting patterns. In this paper, we focus on complementary pattern formation mechanisms that operate even when the diffusion rates are equal. In particular, we can say that when the mean-field ODE has an attracting periodic orbit then the stochastic spatial model will have large-scale spatial structures in equilibrium. We explore this mechanism in depth through the dynamics of the simulator WATOR. (C) 2000 Academic Press.

AB - It is well known that if reacting species experience unequal diffusion rates, then dynamics that lead to a constant steady state in a 'well-mixed' environment can in a spatial setting lead to interesting patterns. In this paper, we focus on complementary pattern formation mechanisms that operate even when the diffusion rates are equal. In particular, we can say that when the mean-field ODE has an attracting periodic orbit then the stochastic spatial model will have large-scale spatial structures in equilibrium. We explore this mechanism in depth through the dynamics of the simulator WATOR. (C) 2000 Academic Press.

UR - http://www.scopus.com/inward/record.url?scp=0034698010&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034698010&partnerID=8YFLogxK

U2 - 10.1006/jtbi.2000.2061

DO - 10.1006/jtbi.2000.2061

M3 - Article

C2 - 10873432

AN - SCOPUS:0034698010

SN - 0022-5193

VL - 205

SP - 201

EP - 214

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

IS - 2

ER -

Lessons on pattern formation from planet WATOR

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this