From integrability to chaos in a Lotka-Volterra cellular automaton

R. Hirota, M. Iwao, A. Ramani, Daisuke Takahashi, B. Grammaticos, Y. Ohta

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

We present a cellular automaton equivalent for the two-dimensional Lotka-Volterra system. The dynamics is studied for integer and rational values of the parameters. In the case of integer parameters the motion is perfectly regular leading to strictly periodic motion. This is still true in the case of rational parameters, but for rational initial conditions the period becomes progressively longer as the denominator of the initial data increases. The motion, in this case, progressively loses its regularity resulting in chaotic behavior in the limit of irrational data.

Original languageEnglish
Pages (from-to)39-44
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume236
Issue number1-2
Publication statusPublished - 1997 Dec 1
Externally publishedYes

Fingerprint

cellular automata
chaos
integers
regularity

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

From integrability to chaos in a Lotka-Volterra cellular automaton. / Hirota, R.; Iwao, M.; Ramani, A.; Takahashi, Daisuke; Grammaticos, B.; Ohta, Y.

In: Physics Letters, Section A: General, Atomic and Solid State Physics, Vol. 236, No. 1-2, 01.12.1997, p. 39-44.

Research output: Contribution to journalArticle

Hirota, R. ; Iwao, M. ; Ramani, A. ; Takahashi, Daisuke ; Grammaticos, B. ; Ohta, Y. / From integrability to chaos in a Lotka-Volterra cellular automaton. In: Physics Letters, Section A: General, Atomic and Solid State Physics. 1997 ; Vol. 236, No. 1-2. pp. 39-44.
@article{4206111c1df548f698e5372382cbac99,
title = "From integrability to chaos in a Lotka-Volterra cellular automaton",
abstract = "We present a cellular automaton equivalent for the two-dimensional Lotka-Volterra system. The dynamics is studied for integer and rational values of the parameters. In the case of integer parameters the motion is perfectly regular leading to strictly periodic motion. This is still true in the case of rational parameters, but for rational initial conditions the period becomes progressively longer as the denominator of the initial data increases. The motion, in this case, progressively loses its regularity resulting in chaotic behavior in the limit of irrational data.",
author = "R. Hirota and M. Iwao and A. Ramani and Daisuke Takahashi and B. Grammaticos and Y. Ohta",
year = "1997",
month = "12",
day = "1",
language = "English",
volume = "236",
pages = "39--44",
journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",
issn = "0375-9601",
publisher = "Elsevier",
number = "1-2",

}

TY - JOUR

T1 - From integrability to chaos in a Lotka-Volterra cellular automaton

AU - Hirota, R.

AU - Iwao, M.

AU - Ramani, A.

AU - Takahashi, Daisuke

AU - Grammaticos, B.

AU - Ohta, Y.

PY - 1997/12/1

Y1 - 1997/12/1

N2 - We present a cellular automaton equivalent for the two-dimensional Lotka-Volterra system. The dynamics is studied for integer and rational values of the parameters. In the case of integer parameters the motion is perfectly regular leading to strictly periodic motion. This is still true in the case of rational parameters, but for rational initial conditions the period becomes progressively longer as the denominator of the initial data increases. The motion, in this case, progressively loses its regularity resulting in chaotic behavior in the limit of irrational data.

AB - We present a cellular automaton equivalent for the two-dimensional Lotka-Volterra system. The dynamics is studied for integer and rational values of the parameters. In the case of integer parameters the motion is perfectly regular leading to strictly periodic motion. This is still true in the case of rational parameters, but for rational initial conditions the period becomes progressively longer as the denominator of the initial data increases. The motion, in this case, progressively loses its regularity resulting in chaotic behavior in the limit of irrational data.

UR - http://www.scopus.com/inward/record.url?scp=0011989512&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011989512&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0011989512

VL - 236

SP - 39

EP - 44

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 1-2

ER -