WOLFRAM SYSTEM MODELER

5th Scenario

# 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:

1. Cellier, F.E. (1991), Continuous System Modeling, Springer-Verlag, New York, ISBN: 0-387-97502-0, 755p.
2. 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 Value: 200000000.0 Type: Real Description: Pollution in 1900 Value: 900000000000.0 Type: Real (ton) Description: Unrecoverable natural resources in 1900 Value: 400000000.0 Type: Real (dollar) Description: Capital investment in 1900 Value: 0.2 Type: Real Description: Proportion of capital investment in agriculture in 1900 Value: 0.04 Type: Real (1/yr) Description: Normal birth rate Value: 0.3 Type: Real (dollar) Description: CIAF normalization Value: 15.0 Type: Real (yr) Description: CIAF time constant Value: 0.025 Type: Real (dollar/yr) Description: Normal capital discard Value: 0.05 Type: Real (dollar/yr) Description: Normal capital generation Value: 1.0 Type: Real (dollar) Description: Capital normalization Value: 1.0 Type: Real (kg/yr) Description: Food coefficient Value: 1.0 Type: Real (kg/yr) Description: Food normalization Value: 135000000.0 Type: Real (hectare) Description: Area of arable land Value: 900000000000.0 Type: Real (ton) Description: Initial natural resources Value: 3599900000.0 Type: Real Description: Standard pollution Value: 26.5 Type: Real (1/hectare) Description: Normal population density Value: 1.0 Type: Real Description: Standard quality of life

# Outputs (6)

Pop Type: Real Description: World population Type: Real Description: Pollution Type: Real Description: Pollution ratio Type: Real (dollar) Description: Capital investment Type: Real Description: Quality of life Type: Real (ton) Description: Natural unrecoverable resources

# Components (78)

Source1 Type: Source Description: This is the (dummy) source model of System Dynamics Type: Rate_1 Description: Unrestricted rate element with one influencing variable Type: Reverse_Level Description: Level of the System Dynamics methodology with time reversal Type: Rate_1 Description: Unrestricted rate element with one influencing variable Type: Sink Description: This is the (dummy) sink model of System Dynamics Type: Source Description: This is the (dummy) source model of System Dynamics Type: Rate_1 Description: Unrestricted rate element with one influencing variable Type: Reverse_Level Description: Level of the System Dynamics methodology with time reversal Type: Rate_1 Description: Unrestricted rate element with one influencing variable Type: Sink Description: This is the (dummy) sink model of System Dynamics Type: Const Description: A constant factor Type: Tabular Description: Tabular function Type: Tabular Description: Tabular function Type: Gain Description: Gain factor Type: Prod_5 Description: Product of five influencing factors Type: Prod_5 Description: Product of five influencing factors Type: Tabular Description: Tabular function Type: Tabular Description: Tabular function Type: Tabular Description: Tabular function Type: Tabular Description: Tabular function Type: Tabular Description: Tabular function Type: Tabular Description: Tabular function Type: Gain Description: Gain factor Type: Prod_2 Description: Product of two influencing factors Type: Tabular Description: Tabular function Type: Source Description: This is the (dummy) source model of System Dynamics Type: Rate_1 Description: Unrestricted rate element with one influencing variable Type: Reverse_Level Description: Level of the System Dynamics methodology with time reversal Type: Rate_1 Description: Unrestricted rate element with one influencing variable Type: Sink Description: This is the (dummy) sink model of System Dynamics Type: Gain Description: Gain factor Type: Prod_2 Description: Product of two influencing factors Type: Gain Description: Gain factor Type: Tabular Description: Tabular function Type: Gain Description: Gain factor Type: Gain Description: Gain factor Type: Gain Description: Gain factor Type: Prod_3 Description: Product of three influencing factors Type: Tabular Description: Tabular function Type: Division Description: Output first input divided by second input Type: Source Description: This is the (dummy) source model of System Dynamics Type: Rate_1 Description: Unrestricted rate element with one influencing variable Type: Reverse_Level Description: Level of the System Dynamics methodology with time reversal Type: Rate_1 Description: Unrestricted rate element with one influencing variable Type: Sink Description: This is the (dummy) sink model of System Dynamics Type: Linear Description: Linear function Type: Gain Description: Gain factor Type: Tabular Description: Tabular function Type: Prod_3 Description: Product of three influencing factors Type: Gain Description: Gain factor Type: Source Description: This is the (dummy) source model of System Dynamics Type: Rate_1 Description: Unrestricted rate element with one influencing variable Type: Reverse_Level Description: Level of the System Dynamics methodology with time reversal Type: Rate_1 Description: Unrestricted rate element with one influencing variable Type: Sink Description: This is the (dummy) sink model of System Dynamics Type: Gain Description: Gain factor Type: Gain Description: Gain factor Type: Prod_2 Description: Product of two influencing factors Type: Division Description: Output first input divided by second input Type: Prod_2 Description: Product of two influencing factors Type: Tabular Description: Tabular function Type: Tabular Description: Tabular function Type: Tabular Description: Tabular function Type: Tabular Description: Tabular function Type: Prod_2 Description: Product of two influencing factors Type: Gain Description: Gain factor Type: Tabular Description: Tabular function Type: Tabular Description: Tabular function Type: Division Description: Output first input divided by second input Type: Tabular Description: Tabular function Type: Tabular Description: Tabular function Type: Prod_4 Description: Product of four influencing factors Type: Tabular Description: Tabular function Type: Tabular Description: Tabular function Type: Gain Description: Gain factor Type: Parameter_Change Description: Parameter variation of WORLD2 model Type: Parameter_Change Description: Parameter variation of WORLD2 model Type: Parameter_Change Description: Parameter variation of WORLD2 model