Bifurcation in a Discrete-Time Piecewise Constant Dynamical System

Table 23

(𝑧−2,𝑧−1)∈𝐽^(𝑘)𝐽^(𝑝)×𝐽^(𝑙)𝐽^(𝑚)	(𝐾^(𝑘)𝐾^(𝑝)×𝐾^(𝑙)𝐾^(𝑚))
B1⇒(𝑧2𝑘,𝑧2𝑘+1)∈𝑅^−𝜎𝑅^−𝜎×𝑅^+𝜎𝑅^+𝜎	𝑅^+𝜎𝑅^+𝜎×𝑅^−𝜎𝑅^−𝜎
B2⇒(𝑧2𝑘,𝑧2𝑘+1)∈𝑅^−𝜎𝐽^(𝑝−𝑘−1)×𝐽^(𝑙−𝑘−1)𝑅^+𝜎	𝑅^+𝜎𝐾^(𝑝−𝑘−1)×𝐾^(𝑙−𝑘−1)𝑅^−𝜎
B3⇒(𝑧2𝑝,𝑧2𝑝+1)∈𝐽^(𝑘−𝑝−1)𝑅^−𝜎×𝑅^+𝜎𝐽^(𝑚−𝑝−1)	𝐾^(𝑘−𝑝−1)𝑅^+𝜎×𝑅^−𝜎𝐾^(𝑚−𝑝−1)
B4⇒(𝑧2𝑝,𝑧2𝑝+1)∈𝐽^(𝑘−𝑝−1)𝑅^−𝜎×𝑅^+𝜎𝐽^(𝑚−𝑝−1)	𝐾^(𝑘−𝑝−1)𝑅^+𝜎×𝑅^−𝜎𝐾^(𝑚−𝑝−1)
B5⇒(𝑧2𝑝,𝑧2𝑝+1)∈𝑅^+𝜎𝑅^−𝜎×𝑅^+𝜎𝑅^−𝜎	𝑅^−𝜎𝑅^+𝜎×𝑅^−𝜎𝑅^+𝜎
B6⇒(𝑧2𝑙,𝑧2𝑙+1)∈𝐽^(𝑘−𝑙−1)𝑅^+𝜎×𝑅^−𝜎𝐽^(𝑚−𝑙−1)	𝐾^(𝑘−𝑙−1)𝑅^−𝜎×𝑅^+𝜎𝐾^(𝑚−𝑙−1)
B7⇒(𝑧2𝑙,𝑧2𝑙+1)∈𝑅^+𝜎𝑅^+𝜎×𝑅^−𝜎𝑅^−𝜎	𝑅^−𝜎𝑅^−𝜎×𝑅^+𝜎𝑅^+𝜎
B8⇒(𝑧2𝑙,𝑧2𝑙+1)∈𝑅^−𝜎𝑅^+𝜎×𝑅^−𝜎𝑅^+𝜎	𝑅^+𝜎𝑅^−𝜎×𝑅^+𝜎𝑅^−𝜎
B9⇒(𝑧2𝑚,𝑧2𝑚+1)∈𝑅^+𝜎𝐽^(𝑝−𝑚−1)×𝐽^(𝑙−𝑚−1)𝑅^−𝜎	𝑅^−𝜎𝐾^(𝑝−𝑚−1)×𝐾^(𝑙−𝑚−1)𝑅^+𝜎
B10⇒(𝑧2𝑚,𝑧2𝑚+1)∈𝑅^−𝜎𝐽^(𝑝−𝑚−1)×𝐽^(𝑙−𝑚−1)𝑅^+𝜎	𝑅^+𝜎𝐾^(𝑝−𝑚−1)×𝐾^(𝑙−𝑚−1)𝑅^−𝜎
B11⇒(𝑧2𝑝,𝑧2𝑝+1)∈𝑅^+𝜎𝑅^−𝜎×𝑅^+𝜎𝑅^−𝜎	𝑅^−𝜎𝑅^+𝜎×𝑅^−𝜎𝑅^+𝜎
B12⇒(𝑧2𝑙,𝑧2𝑙+1)∈𝑅^−𝜎𝑅^+𝜎×𝑅^−𝜎𝑅^+𝜎	𝑅^+𝜎𝑅^−𝜎×𝑅^+𝜎𝑅^−𝜎