scholarly journals Global attractivity of a discrete competition model of plankton allelopathy with infinite deviating arguments

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Xiangdong Xie ◽  
Yalong Xue ◽  
Runxin Wu
Keyword(s):  
Global Attractivity ◽  
Competition Model ◽  
Deviating Arguments ◽  
Plankton Allelopathy

scholarly journals Global Attractivity in a Discrete Mutualism Model with Infinite Deviating Arguments

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Xiangdong Xie ◽  
Yalong Xue ◽  
Runxin Wu
Keyword(s):  
Global Attractivity ◽  
Sufficient Conditions ◽  
Deviating Arguments ◽  
Mutualism Model

A set of sufficient conditions is obtained for the global attractivity of the following two-species discrete mutualism model with infinite deviating arguments: x1(k+1)=x1kexp⁡r1(K1+α1∑s=0+∞J2sx2k-s)/(1+∑s=0+∞J2sx2k-s)-x1k and  x2(k+1)=x2kexp⁡r2(K2+α2∑s=0+∞J1sx1k-s)/(1+∑s=0+∞J1sx1k-s)-x2k, where ri,Ki,αi, i=1,2, are all positive constants, ∑j=1+∞Ji(n)=1, and αi>Ki. Our results generalize the main result of Yang et al. (2014).

scholarly journals Permanence for the Discrete Competition Model with Infinite Deviating Arguments

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Baoguo Chen
Keyword(s):  
Discrete Model ◽  
Sufficient Conditions ◽  
Competition Model ◽  
Deviating Arguments

Sufficient conditions are obtained for the permanence of the following discrete model of competition:x1k+1=x1(k)exp {r1kK1k+α1k∑s=0+∞J2sx2k-s/1+∑s=0+∞J2sx2k-s-x1k-δ1k};x2(k+1)=x2(k)exp {r2kK2k+α2k∑s=0+∞J1sx1k-s/1+∑s=0+∞J1sx1k-s-x2k-δ2k}, whereri,Ki,αi,Ji, andδi,i=1,2, are nonnegative sequences bounded above and below by positive constants, andKi>αi,i=1,2.

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