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INDEX OF FIGURES AND TABLES

Figure 1.1: Interdependence of signals and actions .............................................. 8

Figure 12: Classification of different dynamic choice model approaches ........... 17

Figure 1.3: The master equation point of view the relationship between the

micro and macrolevel in decision processes ...................................... 18

Figure II. 1 : a) Phase diagram of ySu and I for the case of an undamped

cyclic motion (c = 0.8; a = 1; B = 1; v = 1.2); b) Plot of

dY/dt = 0 [-] and dI/dt = 0 [- - -] .................................................. 37

Figure II.2: Effect of an exogenous disruption of Y = 5 at t = 20 ......................... 38

Figure II.3: Graphical solutions of the functions FI = 0 and F2 = 0: [-1;

(a) FI = 0 for small a2: [ ....... ]; (b) FI = 0 for large a2: [- - -] ........... .49

Figure II.4: Domain Dc with interior boundary Ci and exterior boundary Ce. All trajectories enter Dc and remain in Dc according to the

arrows showing the direction of the flux ........................................... 53

Figure II.5: (a) Trajectories in the Y-x plane approaching the one stable focus at the singular point Po for al = 0.09 ; a2 = 0.1; 1= 1.0;

yo = 100; (b) Paths of x(t) and Y(t) for the parameters of (a) ......... 56

Figure II.6: (a) Trajectories in the Y-x plane for al = 0.11; a2 = 0.1;

1 = 1.0; Yo = 100; (b) Paths of x(t) and Y(t) for the parameters

of (a) ................................................................................................ 56

Figure II.7: (a) Trajectories in the Y-x plane for al = 0.11; a2 = 0.4; 1= 1;

yo = 100; (b) Paths ofx(t) and Y(t) for the parameters of (a) .......... 57

128

Figure 11.8 (a) Trajectories in the Y-x plane for al = 0.11; a2 = 0.4;

Y = 2.0; yo = 100; (b) Paths of x(t) and yet) for the

parameters of (a) .............................................................................. 58

Figure ll.9: (a) Trajectories in the Y-x plane for al = 0.18; a2 = 0.4; Y= 0.5;

yo = 100; (b) Paths of x(t) and yet) for the parameters of (a) ....... .59

Figure ll.10: (a) Trajectories in the Y-x plane for al = 0.17; a2 = 1.3; 'Y= 4.0;

yo = 100; with the initial values Yo = 55, XO = 0.25; (b) Paths

of x(t) and yet) for the parameters of (a) ....................................... 60

Figure 11.11: (a) Trajectories in the Y-x plane for al = 0.17; a2 = 1.3; Y = 4;

yo = 100; with the initial values Yo = 52, Xo = - 0.25; (b) Paths

of x(t) and yet) for the parameters of (a) ......................................... 60

Figure 11.12: Graphical solutions of the functions F} = 0 and F2 = 0: L-J; (a) FI = 0 for small a2: [ ....... ] (one singular point); (b) F} = 0 in the marginal case L _ -1 (3 singular points); (c) FI = 0 for

large a2: [- - - ] (5 singular points) ................................................... 70

Figure ll.13: (a) Trajectories in the q-x plane for al = 0.1; a2 = 1.0; bl=0.07;

b2=1.2; 1-1.0; (b) Paths of x(t) and q(t) for the parameters of

(a) ........................................................•..........•............•................... 74

Figure ll.14: (a) Trajectories in the q-x plane for al = 0.15; a2 = 1.0;

bl=O.07; b2=1.2; 1-1.0; (b) Paths of x(t) and q(t) for the

parameters of (a) .............................................................................. 75

Figure 11.15: (a) Trajectories in the q-x plane for al = 0.1; a2 = 1.0;

bl = 0.12; b2 = 1.2; Y = 1.0; (b) Paths of x(t) and q(t) for the

parameters of (a) .............................................................................. 75


bl = 0.07; bl = 1.2; Y =1.0; (b) Paths of x(t) and q(t) for the

parameters of (a) .............................................................................. 76

129


bl = 0.07; b2 = 1.3; 'Y =1.0; (b) Paths of x(t) and q(t) for the

parameters of (a) .............................................................................. 76


bl = 0.07; b2 = 1.5; y:=1.0; with the initial values qo = - 0.5; Xo = - 0.1; (b) Paths of x(t) and q(t) for the parameters of (a) ........ 77

Figure 11.19: (a) Trajectories in the q-x plane for al = 0.1; a2 = 1.5; b l=O.07;

b2=1.5; y:=1.0; with the initial values qo = 0.5; XQ = 0.1; (b)

Paths ofx(t) and q(t) for the parameters of (a) ................................ 77

Figure 11.20: (a) Paths of x(t), q(t) and wet) for al = 0.04; a2 = 0.8; bl = 0.05;

b2 = 5; ci = 0.005; c2 = 0.5; 'Y = 2; 1<: = 2. (b) Trajectories of

x(t) and q(t) in the x-q plane for the parameters of (a) ...................... 85


b2 = 5; ci = 0.005; c2 = 0.5; 'Y = 2; 1<: = 2. (b) Trajectories of



b2 = 5; cl = 0.005; c2 = 0.5; 'Y = 2; 1<: = 2. (b) Trajectories of


Figure 11.23: (a) Paths of x(t), q(t) and wet) for al = 0.04; a2 = 0.8; b l = 0.05;

b2 = 5; CI = 0.0053; c2 = 0.5; 'Y = 2; 1<: = 2. (b) Trajectories of

x(t) and q(t) in the x-q plane for the parameters of (a) ............. : ........ 87


b2 = 5; ci = 0.0055; c2 = 0.5; 'Y = 2; 1<: = 2. and an initial excess

demand > 0 (b) Paths of x(t), q(t) and wet) for the same

parameters and an initial excess demand < 0 ..................................... 88

Figure 11.25: The Lorenz attractor as an example for a strange attractor ................ 90

Figure 11.26: (a) Trajectories in the q-x-plane for ci = 0.023; (b) Fourier

spectrum for ci = 0.023; (c) Time evolution of x for ci = 0.023 ....... 93

130

Figure I1.27: (a) Trajectories in the q-x-plane for cl = 0.025; (b) Fourier

spectrum for cl = 0.025; (c) Time evolution of x for cl = 0.025 ....... 94


spectrum for cl = 0.0255; (c) Time evolution of x for

cl = 0.0255 ....................................................................................... 95


spectrum for cl = 0.03 (c) Time evolution of x for cl = 0.03 ............ 96

Figure I1.30: Strange attractor of the present system in the q-x-w state with

the parameters of Figure I1.29 .......................................................... 97

Figure 11.31: Distance of two initially closed trajectories on the strange

attractor from Figure I1.29 and I1.30 ................................................. 99

Figure I1.32: Determination of the correlation dimension Dc of the strange

attractor from Figure I1.29 and I1.30 ............................................... 1 00

Figure m.1: Plot of the basic time series. BSPR: total volume of real production; CPR: real consumption; IAR: real investment.. ............ 103

Figure I11.2: Plot of the trend corrected and smoothed basic time series ............. 103

Figure I11.3: Plot of the trend corrected, smoothed and normalized basic time

series .............................................................................................. 105

Figure III.4: The business climate as an early indicator for investment

demand ........................................................................................... 109

Figure III.5: Time series of the business climate and the planned production

as indicators for the microeconomic investment and the

production climate .......................................................................... 110

Table I1.1: Lyapunov spectrum for the system of Chapter ITA ........................... 98

131

Table ill. 1: Parameters for the empirical macroeconomic time series

according to Equations II.72 and 11.73 ............................................ 105

Table III.2: Parameters for the empirical macroeconomic time series

according to Equations II.74 and II.75 ............................................ 105

Table ill.3: Parameters for the empirical microeconomic time series


Table IlIA: Parameters for the empirical microeconomic time series


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