Stability of the Trinomial Linear Difference Equations with Two Delays

Global Stability of a Discrete Population Dynamics Model with Two Delays

“…The local stability of the stationary solution x n ≡ α − 1 β + 1 of Eq. (1) for α > 1 and 0 β < 1, as mentioned in the Introduction, is implied by the results of [15,16]. We now show that lim x n = α − 1 β + 1 as n → ∞ under any initial conditions (11).…”

“…(1) for different coprime delays k and m. The Figure 1 shows the results of Theorems 1, 2, and [14,16]. In particular, condition (8) is assumed to be sufficient for the global stability of Eq.…”

“…The local stability of Eq. (10) for arbitrary coefficients a, b ∈ R and delays k, m ∈ N is studied in [15,16].…”

Stability of a delay difference system

“…Theorem 1.1 (see [7,Theorem 2]). The zero solution of (1.2) It follows from Cohn's results [3] that (1.2) is asymptotically stable provided that…”

“…They established that the equation is asymptotically stable if and only if 2sin(π/2(2k − 1)) > −b > 0. Scalar equation with two delays x n = ax n−m + bx n−k , more compound than (1.2), was investigated by Dannan [5], Kipnis and Nigmatulin [7], and Nikolaev [13,14]. The matrix equation…”