*4.1. Fundamental Demand*

We investigate the dynamics starting from the analytical results. In the asymptotic stability region, prices go to one of the fixed points with speed according to the parameters. Closer the parameters to the border of the stability region slower the convergence, as it can be seen in Figure 4, comparing the scenario in the top with parameters *a* = 1, *b* = 1.9 and *c* = 0.4 to that in the bottom with *a* = 1, *b* = 0.7 and *c* = 1.4, where the value of *c* at the border would be <sup>1</sup> *<sup>b</sup>* = 1.4286. Each figure in the following shows price dynamics on the left-hand side and the phase space (*x*, *y*) on the right-hand side. Outside the stability region, the dynamic scenarios include periodic orbits and chaotic motion. Some examples of periodic orbits are reported in Figure 5, where on the top there is an orbit of period 6 to be read clockwise; note that in terms of price and demand the orbit is 3-period but they are combined giving 6 couples of price and demand. On the bottom a periodic elliptic orbit appears, this dynamics holds for any value of *a* ∈ (0, 1) when *b* and *c* are equal 1. In this case, the effect of the demand is fixed, while the price drift matters: the higher *a* the closer the ellipse center to the fixed point (*v*, 0) and the closer the amplitude to the range (*v* − *δ*, *v* + *δ*). Examples of chaotic motion are reported in Figures 6 and 7. In Figure 6 the plot on the top panel shows prices almost regularly oscillating in the range (*v* − *δ*, *v* + *δ*), since parameters are closed to the stability region border; while on the bottom panel parameters are far from the border and prices oscillate widely. In Figure 7, *c* is negative; being *c* the fundamental demand parameter, negative values mimic a trend follower demand, indeed the dynamics show bear and bull period (on the top), a wide range of prices (in the center) and price overvaluation (on the bottom). In Figure 8 bifurcation diagrams with respect *c* show the map behavior varying *c*.
