### 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 language | English |
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Pages (from-to) | 39-44 |

Number of pages | 6 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 236 |

Issue number | 1-2 |

Publication status | Published - 1997 Dec 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*236*(1-2), 39-44.

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

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 236, no. 1-2, pp. 39-44.

}

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 -