TY - JOUR

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

AU - Hirota, R.

AU - Iwao, M.

AU - Ramani, A.

AU - Takahashi, D.

AU - Grammaticos, B.

AU - Ohta, Y.

N1 - Funding Information:
Y. Ohta acknowledges the financial support of the Japan Ministry of Education through the Foreign Study Program.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

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.

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U2 - 10.1016/S0375-9601(97)00721-4

DO - 10.1016/S0375-9601(97)00721-4

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 -