Permanence of a Discrete Model of Mutualism with Infinite Deviating Arguments

Xuepeng Li and Wensheng Yang

Discrete Dynamics in Nature and Society, 2010, vol. 2010, 1-7

Abstract:

We propose a discrete model of mutualism with infinite deviating arguments, that is ð ‘¥ 1 ( ð ‘› + 1 ) = ð ‘¥ 1 ( ð ‘› ) e x p { ð ‘Ÿ 1 ( ð ‘› ) [ ( ð ¾ 1 ( ð ‘› ) + ð ›¼ 1 ∑ ( ð ‘› ) ∞ ð ‘ = 0 ð ½ 2 ( ð ‘ ) ð ‘¥ 2 ∑ ( ð ‘› − ð ‘ ) ) / ( 1 + ∞ ð ‘ = 0 ð ½ 2 ( ð ‘ ) ð ‘¥ 2 ( ð ‘› − ð ‘ ) ) − ð ‘¥ 1 ( ð ‘› − 𠜎 1 ( ð ‘› ) ) ] } , ð ‘¥ 2 ð ‘¥ ( ð ‘› + 1 ) = 2 ( ð ‘› ) e x p { ð ‘Ÿ 2 ( ð ‘› ) [ ( ð ¾ 2 ( ð ‘› ) + ð ›¼ 2 ∑ ( ð ‘› ) ∞ ð ‘ = 0 ð ½ 1 ( ð ‘ ) ð ‘¥ 1 ∑ ( ð ‘› − ð ‘ ) ) / ( 1 + ∞ ð ‘ = 0 ð ½ 1 ( ð ‘ ) ð ‘¥ 1 ( ð ‘› − ð ‘ ) ) − ð ‘¥ 2 ( ð ‘› − 𠜎 2 ( ð ‘› ) ) ] } . By some Lemmas, sufficient conditions are obtained for the permanence of the system.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:931798

DOI: 10.1155/2010/931798

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