Discrete Dynamics in Nature and Society

Research Article

Complete Asymptotic Analysis of a Two-Nation Arms Race Model with Piecewise Constant Nonlinearities

Table 10

Initial conditionConditionConclusion
𝐴 ( 𝑝 , 𝜆 ) × 𝐵 ( 𝜆 , 𝑚 ) 0 ≤ 𝑝 ≤ 𝑚 ( 𝑧 2 𝑝 , 𝑧 2 𝑝 + 1 ) ∈ 𝐵 × 𝐵
𝐴 ( 𝑝 , 𝜆 ) × 𝐵 ( 𝜆 , 𝑚 ) 0 ≤ 𝑚 < 𝑝 ( 𝑧 2 𝑚 , 𝑧 2 𝑚 + 1 ) ∈ 𝐴 × 𝐶
𝐶 ( 𝜆 , 𝑝 ) × 𝐵 ( 𝑚 , 𝜆 ) 0 ≤ 𝑝 ≤ 𝑚 ( 𝑧 2 𝑝 , 𝑧 2 𝑝 + 1 ) ∈ 𝐵 × 𝐵
𝐶 ( 𝜆 , 𝑝 ) × 𝐵 ( 𝑚 , 𝜆 ) 0 ≤ 𝑚 < 𝑝 ( 𝑧 2 𝑚 , 𝑧 2 𝑚 + 1 ) ∈ 𝐶 × 𝐴
𝐷 ( 𝑝 , 𝜆 ) × 𝐴 ( 𝜆 , 𝑚 ) 0 ≤ 𝑝 ≤ 𝑚 ( 𝑧 2 𝑝 , 𝑧 2 𝑝 + 1 ) ∈ 𝐶 × 𝐴
𝐷 ( 𝑝 , 𝜆 ) × 𝐴 ( 𝜆 , 𝑚 ) 0 ≤ 𝑚 < 𝑝 ( 𝑧 2 𝑚 , 𝑧 2 𝑚 + 1 ) ∈ 𝐷 × 𝐷
𝐵 ( 𝑝 , 𝜆 ) × 𝐶 ( 𝜆 , 𝑚 ) 0 ≤ 𝑝 ≤ 𝑚 ( 𝑧 2 𝑝 , 𝑧 2 𝑝 + 1 ) ∈ 𝐴 × 𝐶
𝐵 ( 𝑝 , 𝜆 ) × 𝐶 ( 𝜆 , 𝑚 ) 0 ≤ 𝑚 < 𝑝 ( 𝑧 2 𝑚 , 𝑧 2 𝑚 + 1 ) ∈ 𝐵 × 𝐵
𝐴 ( 𝜆 , 𝑝 ) × 𝐷 ( 𝑚 , 𝜆 ) 0 ≤ 𝑝 ≤ 𝑚 ( 𝑧 2 𝑝 , 𝑧 2 𝑝 + 1 ) ∈ 𝐷 × 𝐷
𝐴 ( 𝜆 , 𝑝 ) × 𝐷 ( 𝑚 , 𝜆 ) 0 ≤ 𝑚 < 𝑝 ( 𝑧 2 𝑚 , 𝑧 2 𝑚 + 1 ) ∈ 𝐴 × 𝐶
𝐶 ( 𝑝 , 𝜆 ) × 𝐷 ( 𝜆 , 𝑚 ) 0 ≤ 𝑝 ≤ 𝑚 ( 𝑧 2 𝑝 , 𝑧 2 𝑝 + 1 ) ∈ 𝐷 × 𝐷
𝐶 ( 𝑝 , 𝜆 ) × 𝐷 ( 𝜆 , 𝑚 ) 0 ≤ 𝑚 < 𝑝 ( 𝑧 2 𝑚 , 𝑧 2 𝑚 + 1 ) ∈ 𝐶 × 𝐴
𝐵 ( 𝜆 , 𝑝 ) × 𝐴 ( 𝑚 , 𝜆 ) 0 ≤ 𝑝 ≤ 𝑚 ( 𝑧 2 𝑝 , 𝑧 2 𝑝 + 1 ) ∈ 𝐶 × 𝐴
𝐵 ( 𝜆 , 𝑝 ) × 𝐴 ( 𝑚 , 𝜆 ) 0 ≤ 𝑚 < 𝑝 ( 𝑧 2 𝑚 , 𝑧 2 𝑚 + 1 ) ∈ 𝐵 × 𝐵
𝐷 ( 𝜆 , 𝑝 ) × 𝐶 ( 𝑚 , 𝜆 ) 0 ≤ 𝑝 ≤ 𝑚 ( 𝑧 2 𝑝 , 𝑧 2 𝑝 + 1 ) ∈ 𝐴 × 𝐶
𝐷 ( 𝜆 , 𝑝 ) × 𝐶 ( 𝑚 , 𝜆 ) 0 ≤ 𝑚 < 𝑝 ( 𝑧 2 𝑚 , 𝑧 2 𝑚 + 1 ) ∈ 𝐷 × 𝐷