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

Table 2

Initial condition	Condition	Conclusion
(𝑧−2,𝑧−1)∈𝐵^(𝑘)×𝐶^(𝑠,𝑝)	0≤𝑘≤𝑝	(𝑧2𝑘,𝑧2𝑘+1)∈𝐴×𝐶
(𝑧−2,𝑧−1)∈𝐵^(𝑘)×𝐶^(𝑠,𝑝)	0≤𝑝<𝑘	(𝑧2𝑝,𝑧2𝑝+1)∈𝐵×𝐵
(𝑧−2,𝑧−1)∈𝐵^(𝑘)×𝐷^(𝑝)	0≤𝑘≤𝑝	(𝑧2𝑘,𝑧2𝑘+1)∈𝐴×𝐷
(𝑧−2,𝑧−1)∈𝐵^(𝑘)×𝐷^(𝑝)	0≤𝑝<𝑘	(𝑧2𝑝,𝑧2𝑝+1)∈𝐵×𝐴
(𝑧−2,𝑧−1)∈𝐶^(𝑠,𝑘)×𝐵^(𝑝)	0≤𝑘≤𝑝	(𝑧2𝑘,𝑧2𝑘+1)∈𝐵×𝐵
(𝑧−2,𝑧−1)∈𝐶^(𝑠,𝑘)×𝐵^(𝑝)	0≤𝑝<𝑘	(𝑧2𝑝,𝑧2𝑝+1)∈𝐶×𝐴
(𝑧−2,𝑧−1)∈𝐷^(𝑘)×𝐶^(𝑝,𝑠)	0≤𝑘≤𝑝	(𝑧2𝑘,𝑧2𝑘+1)∈𝐴×𝐶
(𝑧−2,𝑧−1)∈𝐷^(𝑘)×𝐶^(𝑝,𝑠)	0≤𝑝<𝑘	(𝑧2𝑝,𝑧2𝑝+1)∈𝐷×𝐷
(𝑧−2,𝑧−1)∈𝐷^(𝑘)×𝐵^(𝑝)	0≤𝑘≤𝑝	(𝑧2𝑘,𝑧2𝑘+1)∈𝐴×𝐵
(𝑧−2,𝑧−1)∈𝐷^(𝑘)×𝐵^(𝑝)	0≤𝑝<𝑘	(𝑧2𝑝,𝑧2𝑝+1)∈𝐷×𝐴
(𝑧−2,𝑧−1)∈𝐶^(𝑘,𝑠)×𝐷^(𝑝)	0≤𝑘≤𝑝	(𝑧2𝑘,𝑧2𝑘+1)∈𝐷×𝐷
(𝑧−2,𝑧−1)∈𝐶^(𝑘,𝑠)×𝐷^(𝑝)	0≤𝑝<𝑘	(𝑧2𝑝,𝑧2𝑝+1)∈𝐶×𝐴