WOLFRAM SYSTEM MODELER
Scenario_55th Scenario |
 |
Diagram
Wolfram Language
In[1]:=
SystemModel["SystemDynamics.WorldDynamics.World2.Scenario_5"]
Out[1]:=
Information
This is yet another modification of Jay Forrester's WORLD2 model. We wish to introduce time reversal to the simulation. To this end, we replace the regular continuous levels of the System Dynamics methodology by reversible levels.
References:
- Cellier, F.E. (1991), Continuous System Modeling, Springer-Verlag, New York, ISBN: 0-387-97502-0, 755p.
- Forrester, J.W. (1971), World Dynamics, Pegasus Communications, 160p.
Simulate the model across 233 years with time reversal starting at year 200, i.e., we simulate the world model forward through time from the year 1900 until the year 2100, and then backward through time from the year 2100 until the year 2067. For this experiment, you need to set the simulation accuracy to 1e-10.
Plot the simulated world population against the calendar years.
You shall notice that time reversal in the world model is numerically problematic. The simulation is numerically unstable in backward direction. The time-reversed model simulates correctly for a few years, but as numerical errors get the trajectory away from its designed path, the backward trajectory starts diverging quickly from the forward trajectory.
Parameters (18)
| Population_0 |
Value: 1650000000.0 Type: Real Description: World population in 1900 |
|---|---|
| Pollution_0 |
Value: 200000000.0 Type: Real Description: Pollution in 1900 |
| Nat_Resources_0 |
Value: 900000000000.0 Type: Real (ton) Description: Unrecoverable natural resources in 1900 |
| Cap_Invest_0 |
Value: 400000000.0 Type: Real (dollar) Description: Capital investment in 1900 |
| CIAF_0 |
Value: 0.2 Type: Real Description: Proportion of capital investment in agriculture in 1900 |
| BRN |
Value: 0.04 Type: Real (1/yr) Description: Normal birth rate |
| CIAFN |
Value: 0.3 Type: Real (dollar) Description: CIAF normalization |
| CIAFT |
Value: 15.0 Type: Real (yr) Description: CIAF time constant |
| CIDN |
Value: 0.025 Type: Real (dollar/yr) Description: Normal capital discard |
| CIGN |
Value: 0.05 Type: Real (dollar/yr) Description: Normal capital generation |
| ECIRN |
Value: 1.0 Type: Real (dollar) Description: Capital normalization |
| FC |
Value: 1.0 Type: Real (kg/yr) Description: Food coefficient |
| FN |
Value: 1.0 Type: Real (kg/yr) Description: Food normalization |
| Land_Area |
Value: 135000000.0 Type: Real (hectare) Description: Area of arable land |
| NRI |
Value: 900000000000.0 Type: Real (ton) Description: Initial natural resources |
| POLS |
Value: 3599900000.0 Type: Real Description: Standard pollution |
| Pop_dens_norm |
Value: 26.5 Type: Real (1/hectare) Description: Normal population density |
| QLS |
Value: 1.0 Type: Real Description: Standard quality of life |
Outputs (6)
| Pop |
Type: Real Description: World population |
|---|---|
| Pol |
Type: Real Description: Pollution |
| Pol_rat |
Type: Real Description: Pollution ratio |
| Cap_inv |
Type: Real (dollar) Description: Capital investment |
| Qual_life |
Type: Real Description: Quality of life |
| Nat_res |
Type: Real (ton) Description: Natural unrecoverable resources |
Components (78)
 |
Source1 |
Type: Source |
|---|---|---|
 |
Birth_Rate |
Type: Rate_1 |
 |
Population |
Type: Reverse_Level |
|
Death_Rate |
Type: Rate_1 |
 |
Sink1 |
Type: Sink |
|
Source2 |
Type: Source |
|
Generation |
Type: Rate_1 |
|
Natural_Resources |
Type: Reverse_Level |
|
Depletion |
Type: Rate_1 |
|
Sink2 |
Type: Sink |
 |
Gen_Const |
Type: Const |
 |
BRMM |
Type: Tabular |
|
DRMM |
Type: Tabular |
 |
BR_norm |
Type: Gain |
 |
Prod_5_1 |
Type: Prod_5 |
|
Prod_5_2 |
Type: Prod_5 |
|
BRFM |
Type: Tabular |
|
BRPM |
Type: Tabular |
|
BRCM |
Type: Tabular |
|
DRCM |
Type: Tabular |
|
DRPM |
Type: Tabular |
|
DRFM |
Type: Tabular |
|
Crowd_Rat |
Type: Gain |
 |
Prod_2_1 |
Type: Prod_2 |
|
NRMM |
Type: Tabular |
|
Source3 |
Type: Source |
|
CI_Generation |
Type: Rate_1 |
|
Capital_Investment |
Type: Reverse_Level |
|
CI_Discard |
Type: Rate_1 |
|
Sink3 |
Type: Sink |
|
CIG_norm |
Type: Gain |
|
Prod_2_2 |
Type: Prod_2 |
|
CID_norm |
Type: Gain |
|
CIM |
Type: Tabular |
|
MSL |
Type: Gain |
|
NRFR |
Type: Gain |
|
ECIR |
Type: Gain |
 |
Prod_3_1 |
Type: Prod_3 |
|
NREM |
Type: Tabular |
 |
CIR |
Type: Division |
|
Source4 |
Type: Source |
|
P_Generation |
Type: Rate_1 |
|
Pollution |
Type: Reverse_Level |
|
P_Absorption |
Type: Rate_1 |
|
Sink4 |
Type: Sink |
 |
NotCIAF |
Type: Linear |
|
Pol_Ratio |
Type: Gain |
|
FCM |
Type: Tabular |
|
Prod_3_2 |
Type: Prod_3 |
|
Food_Ratio |
Type: Gain |
|
Source5 |
Type: Source |
|
CIAFG |
Type: Rate_1 |
|
CIAF |
Type: Reverse_Level |
|
CIAFD |
Type: Rate_1 |
|
Sink5 |
Type: Sink |
|
CIAF_D |
Type: Gain |
|
CIAF_G |
Type: Gain |
|
Prod_2_3 |
Type: Prod_2 |
|
P_Abs |
Type: Division |
|
Prod_2_4 |
Type: Prod_2 |
|
POLCM |
Type: Tabular |
|
POLAT |
Type: Tabular |
|
CFIFR |
Type: Tabular |
|
FPM |
Type: Tabular |
|
Prod_2_5 |
Type: Prod_2 |
|
CIRA |
Type: Gain |
|
FPCI |
Type: Tabular |
|
CIQR |
Type: Tabular |
|
QLMF |
Type: Division |
|
QLM |
Type: Tabular |
|
QLF |
Type: Tabular |
 |
Prod_4_1 |
Type: Prod_4 |
|
QLC |
Type: Tabular |
|
QLP |
Type: Tabular |
|
Quality_of_Life |
Type: Gain |
 |
NR_norm |
Type: Parameter_Change |
|
Pol_norm |
Type: Parameter_Change |
|
DR_norm |
Type: Parameter_Change |