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

Figure 14

We take orbits of length 𝑛=10000 of 𝑔_𝛽∘𝑓_𝛼 with initial conditions on the image of the turning points and estimate the Lyapunov exponent for (𝛼,𝛽)∈[1,2]×[0,2] with step size of 0.01. In red we draw those values of the parameter for which the maximum of Lyapunov exponents for the turning points is smaller than or equal to 0.