Speculative behavior and chaotic asset price dynamics: On the emergence of a bandcount accretion bifurcation structure

Figure 1.  (a) Schematic representation of the $ ( \varepsilon, \mu) $ parameter plane; (b)–(g) Sample plots of function $ f $ and its absorbing intervals

Figure 2.  (a) 2D bifurcation diagram in the $ ( \varepsilon, \mu) $ parameter plane of $ f $, with $ a = 1.25 $. (b) Close up of the rectangular area marked in (a)

Figure 3.  1D bifurcation diagram corresponding to the blue arrow in Figure 2(a), with $ \varepsilon = 0.72 $ and $ a = 1.25 $. The critical points $ \ell_{{i}} $, $ \mathit{m}^{-}_{{i}} $, $ \mathit{m}^{+}_{{i}} $ and $ \mathit{r}_{{i}} $ of different ranks are shown by blue, green, orange and red lines, respectively

Figure 4.  Plot of function $ f $ and formation of gaps in the upper part $ B^R $ of the chaotic attractor $ \mathcal{Q} $

Figure 5.  Plot of function $ f $ and formation of gaps in the lower part $ B^L $ of the chaotic attractor $ \mathcal{Q} $

Figure 6.  (a) 2D bifurcation diagram in the $ ( \varepsilon, \mu) $ parameter plane of $ f $, with $ a = 1.25 $, related to a triangular shaped "jut" of chaoticity region $ \mathcal{C}_{2+1} $. (b) Close up of the rectangular area marked in (a)

Figure 7.  1D bifurcation diagram corresponding to the blue arrow marked "1" in Figure 6(b), with $ \varepsilon = 1.37 $ and $ a = 1.25 $. The critical points $ \ell_{{i}} $, $ \mathit{m}^{-}_{{i}} $, $ \mathit{m}^{+}_{{i}} $ and $ \mathit{r}_{{i}} $ of different ranks are shown by blue, green, orange and red lines, respectively

Figure 8.  Plot of function $ f $, with $ a = 1.25 $, $ \varepsilon = 1.37 $ and $ \mu = \tilde{\mu} = -3.44 $. Pink and dark-red lines show the related sequences of preimages of zero

Figure 9.  Plot of function $ f $, with $ a = 1.25 $, $ \varepsilon = 1.37 $ and $ \mu = \tilde{\mu} = -3.454 $. Pink and dark-red lines show the related sequences of preimages of zero

Figure 10.  1D bifurcation diagram corresponding to the blue arrow marked "2" in Figure 6(b), with $ \varepsilon = 1.34 $ and $ a = 1.25 $. The critical points $ \ell_{{i}} $, $ \mathit{m}^{-}_{{i}} $, $ \mathit{m}^{+}_{{i}} $ and $ \mathit{r}_{{i}} $ of different ranks are shown by blue, green, orange and red lines, respectively

Figure 11.  1D bifurcation diagram corresponding to the blue arrow marked "3" in Figure 6(b), with $ \varepsilon = 1.32 $ and $ a = 1.25 $. The critical points $ \ell_{{i}} $, $ \mathit{m}^{-}_{{i}} $, $ \mathit{m}^{+}_{{i}} $ and $ \mathit{r}_{{i}} $ of different ranks are shown by blue, green, orange and red lines, respectively

Figure 12.  The functioning of the financial market model. The panel depicts the dynamics of Figure 9 in the time domain. The parameters are $ \varepsilon = 1.37 $, $ a = 1.25 $, and $ \mu = -3.454 $

Figure 13.  (a) 2D bifurcation diagram in the $ ( \varepsilon, \mu) $ parameter plane of $ f $, with $ a = 1.1 $. (b) Close up of the parallelogram area marked by the dark-red line in (a)