Chaotification for Partial Difference Equations via Controllers

Figure 1

Computer simulation results, where 𝑘=2, 𝑛=0,1,…,20000, and the initial value is 𝑥(0,0)=0.3, 𝑥(0,1)=0.1, and 𝑥(0,2)=0.8. (a) Simple dynamical behaviors for the original system (33); (b) simulation results of the system (29) for 𝜇=4, which shows that there is a dense orbit around the origin and then there are complex dynamical behaviors in (29).

(a)

(b)