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

Table 13

Assumption: (𝑧₋₂,𝑧₋₁)∈𝐷^(𝑘,𝑝)×𝐵^(𝑙,𝑚).

Condition	Conclusion
0≤𝑘=𝑝≤min{𝑙,𝑚}	(𝑧2𝑘,𝑧2𝑘+1)∈𝐵×𝐵
0≤𝑝=𝑙=𝑚<𝑘	(𝑧2𝑝,𝑧2𝑝+1)∈𝐴×𝐶
0≤𝑙=𝑚<min{𝑘,𝑝}	(𝑧2𝑙,𝑧2𝑙+1)∈𝐷×𝐷
0≤𝑙=𝑚=𝑘<𝑝	(𝑧2𝑙𝑧2𝑙+1)∈𝐶×𝐴
0≤𝑝=𝑚<min{𝑘,𝑙}	(𝑧2𝑝,𝑧2𝑝+1)∈𝐴×𝐶
0≤𝑘=𝑙<min{𝑝,𝑚}	(𝑧2𝑘,𝑧2𝑘+1)∈𝐶×𝐴
0≤𝑘<min{𝑝,𝑙,𝑚}	(𝑧2𝑘,𝑧2𝑘+1)∈𝐶^(𝜆,𝑝−𝑘−1)×𝐵^(𝑙−𝑘−1,𝜆)
0≤𝑝<min{𝑘,𝑙,𝑚}	(𝑧2𝑝,𝑧2𝑝+1)∈𝐴^(𝑘−𝑝−1,𝜆)×𝐵^(𝜆,𝑚−𝑝−1)
0≤𝑝=𝑙<min{𝑘,𝑚}	(𝑧2𝑝,𝑧2𝑝+1)∈𝐴^(𝑘−𝑝−1,𝜆)×𝐵^(𝜆,𝑚−𝑝−1)
0≤𝑙<min{𝑝,𝑘,𝑚}	(𝑧2𝑙,𝑧2𝑙+1)∈𝐷^(𝑘−𝑙−1,𝜆)×𝐴^(𝜆,𝑚−𝑙−1)
0≤𝑚<min{𝑝,𝑘,𝑙}	(𝑧2𝑚,𝑧2𝑚+1)∈𝐷^(𝜆,𝑝−𝑚−1)×𝐶^(𝑙−𝑚−1,𝜆)
0≤𝑘=𝑚<min{𝑝,𝑙}	(𝑧2𝑚,𝑧2𝑚+1)∈𝐶^(𝜆,𝑝−𝑘−1)×𝐵^(𝑙−𝑘−1,𝜆)