Dynamics of a Family of Nonlinear Delay Difference Equations - Qiuli He; Taixiang Sun; Hongjian Xi (Abstract and Applied Analysis)
We study the global asymptotic stability of the following difference equation: xn+1=f(xn-k1,xn-k2,…,xn-ks;xn-m1,xn-m2,…,xn-mt),n=0,1,…, where 0≤k1<k2<⋯<ks and 0≤m1<m2<⋯<mt with {k1,k2,…,ks}⋂‍{m1,m2,…,mt}=∅, the initial values are positive, and f∈C(Es+t,(0,+∞)) with E∈{(0,+∞),[0,+∞)}. We give sufficient conditions under which the unique positive equilibrium x- of that equation is globally asymptotically stable.