Bifurcation in a Discrete-Time Piecewise Constant Dynamical System

Table 13

(𝑧−2,𝑧−1)∈𝑅^−𝜎𝐽^(𝑘)×𝐽^(𝑝)𝐼^(𝑙)	(𝐽^(𝑘)𝑅^−𝜎×𝐼^(𝑙)𝐽^(𝑝))
A1⇒(𝑧2𝑘−1,𝑧2𝑘)∈𝐽^(𝑝−𝑘)𝐼^(𝑙−𝑘)×𝑅^−𝜎𝑅^−𝜎	𝐼^(𝑙−𝑘)𝐽^(𝑝−𝑘)×𝑅^−𝜎𝑅^−𝜎
A2⇒(𝑧2𝑘−1,𝑧2𝑘)∈𝐽^(𝑝−𝑘)𝐼^(𝑙−𝑘)×𝑅^−𝜎𝑅^−𝜎	𝐼^(𝑙−𝑘)𝐽^(𝑝−𝑘)×𝑅^−𝜎𝑅^−𝜎
A3⇒(𝑧2𝑙,𝑧2𝑙+1)∈𝑅^−𝜎𝐽^(𝑘−𝑙−1)×𝑅^−𝜎𝑅^−𝜎	𝐽^(𝑘−𝑙−1)𝑅^−𝜎×𝑅^−𝜎𝑅^−𝜎
A4⇒(𝑧2𝑘−1,𝑧2𝑘)∈𝐽^(𝑝−𝑘)𝐼^(𝑙−𝑘)×𝑅^−𝜎𝑅^−𝜎	𝐼^(𝑙−𝑘)𝐽^(𝑝−𝑘)×𝑅^−𝜎𝑅^−𝜎
A5⇒(𝑧2𝑝,𝑧2𝑝+1)∈𝑅^−𝜎𝐽^(𝑘−𝑝−1)×𝑅^−𝜎𝐼^(𝑙−𝑝−1)	𝐽^(𝑘−𝑝−1)𝑅^−𝜎×𝐼^(𝑙−𝑝−1)𝑅^−𝜎
A6⇒(𝑧2𝑙,𝑧2𝑙+1)∈𝑅^−𝜎𝐽^(𝑘−𝑙−1)×𝐽^(𝑝−𝑙−1)𝑅^−𝜎	𝐽^(𝑘−𝑙−1)𝑅^−𝜎×𝑅^−𝜎𝐽^(𝑝−𝑙−1)