The Emergence of Bull and Bear Dynamics in a Nonlinear Model of Interacting Markets

Figure 7

Change of stability in the two-dimensional case. Parameters are 𝑎^𝐻=0.41,𝑏^𝐻=0.11,𝑐^𝐻=0.83,𝛾^𝐻=0.3,𝐹^𝐻=4.279,𝐹^𝑆=6.07,𝑑=0.35, and 𝑓=0.7. In (a), at 𝑒=0.124697, the attractors are the fixed points 𝑃₂ and 𝑂, their basins are bounded by the stable manifold of 𝑃₁. In (b), at 𝑒=2.22, the attractors are 𝑃₁ and 𝑃₂, the border between basins ℬ₁ and ℬ₂ is the stable manifold of the fundamental equilibrium 𝑂.

(a)

(b)