Describing the Dynamics and Complexity of Matsumoto-Nonaka's Duopoly Model

Figure 13

For 𝛼=1.86 we have drawn several different 𝜔-limits. We make 200000 iterations and draw the last 100000 in the 𝑋𝑌 axis. We can see that for these parameter values the function is chaotic, but it could happen that the chaos is not physically observable.

(a) 𝛼=1.86, 𝛽=1.25, 𝑥₀=1/𝛽, and 𝑦₀=1−1/𝛼

(b) 𝛼=1.86, 𝛽=1.54, 𝑥₀=1/𝛽, and 𝑦₀=1−1/𝛼

(c) 𝛼=1.86, 𝛽=1.56, 𝑥₀=1/𝛽, and 𝑦₀=1−1/𝛼

(d) 𝛼=1.86, 𝛽=1.74, 𝑥₀=1/𝛽, and 𝑦₀=1−1/𝛼