Limit 2-Cycles for a Discrete-Time Bang-Bang Control Model

Table 1

Case	𝑦−1	𝑧−1	Condition	lim𝑛(𝑦𝑛,𝑧𝑛)
0>max{𝜉^+0,𝜉^+1}	∈ R	∈ R		(𝜉^+0,𝜉^+1)
0<min{𝜉^−0,𝜉^−1}	∈ R	∈ R		(𝜉^−0,𝜉^−1)
min{𝜉^+0,𝜉^+1}<0<max{𝜉^+0,𝜉^+1}	∈ R	∈ R	𝜉^+0<0<𝜉^+1	(𝜉^−0,𝜉^+1)
			𝜉^+1<0<𝜉^+0	(𝜉^+0,𝜉^−1)
min{𝜉^−0,𝜉^−1}<0<max{𝜉^−0,𝜉^−1}	∈ R	∈ R	𝜉^−0<0<𝜉^−1	(𝜉^−0,𝜉^+1)
			𝜉^−1<0<𝜉^−0	(𝜉^+0,𝜉^−1)