WOLFRAM SYSTEM MODELER

Scenario_5

5th 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:

  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

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

Description: This is the (dummy) source model of System Dynamics

Birth_Rate

Type: Rate_1

Description: Unrestricted rate element with one influencing variable

Population

Type: Reverse_Level

Description: Level of the System Dynamics methodology with time reversal

Death_Rate

Type: Rate_1

Description: Unrestricted rate element with one influencing variable

Sink1

Type: Sink

Description: This is the (dummy) sink model of System Dynamics

Source2

Type: Source

Description: This is the (dummy) source model of System Dynamics

Generation

Type: Rate_1

Description: Unrestricted rate element with one influencing variable

Natural_Resources

Type: Reverse_Level

Description: Level of the System Dynamics methodology with time reversal

Depletion

Type: Rate_1

Description: Unrestricted rate element with one influencing variable

Sink2

Type: Sink

Description: This is the (dummy) sink model of System Dynamics

Gen_Const

Type: Const

Description: A constant factor

BRMM

Type: Tabular

Description: Tabular function

DRMM

Type: Tabular

Description: Tabular function

BR_norm

Type: Gain

Description: Gain factor

Prod_5_1

Type: Prod_5

Description: Product of five influencing factors

Prod_5_2

Type: Prod_5

Description: Product of five influencing factors

BRFM

Type: Tabular

Description: Tabular function

BRPM

Type: Tabular

Description: Tabular function

BRCM

Type: Tabular

Description: Tabular function

DRCM

Type: Tabular

Description: Tabular function

DRPM

Type: Tabular

Description: Tabular function

DRFM

Type: Tabular

Description: Tabular function

Crowd_Rat

Type: Gain

Description: Gain factor

Prod_2_1

Type: Prod_2

Description: Product of two influencing factors

NRMM

Type: Tabular

Description: Tabular function

Source3

Type: Source

Description: This is the (dummy) source model of System Dynamics

CI_Generation

Type: Rate_1

Description: Unrestricted rate element with one influencing variable

Capital_Investment

Type: Reverse_Level

Description: Level of the System Dynamics methodology with time reversal

CI_Discard

Type: Rate_1

Description: Unrestricted rate element with one influencing variable

Sink3

Type: Sink

Description: This is the (dummy) sink model of System Dynamics

CIG_norm

Type: Gain

Description: Gain factor

Prod_2_2

Type: Prod_2

Description: Product of two influencing factors

CID_norm

Type: Gain

Description: Gain factor

CIM

Type: Tabular

Description: Tabular function

MSL

Type: Gain

Description: Gain factor

NRFR

Type: Gain

Description: Gain factor

ECIR

Type: Gain

Description: Gain factor

Prod_3_1

Type: Prod_3

Description: Product of three influencing factors

NREM

Type: Tabular

Description: Tabular function

CIR

Type: Division

Description: Output first input divided by second input

Source4

Type: Source

Description: This is the (dummy) source model of System Dynamics

P_Generation

Type: Rate_1

Description: Unrestricted rate element with one influencing variable

Pollution

Type: Reverse_Level

Description: Level of the System Dynamics methodology with time reversal

P_Absorption

Type: Rate_1

Description: Unrestricted rate element with one influencing variable

Sink4

Type: Sink

Description: This is the (dummy) sink model of System Dynamics

NotCIAF

Type: Linear

Description: Linear function

Pol_Ratio

Type: Gain

Description: Gain factor

FCM

Type: Tabular

Description: Tabular function

Prod_3_2

Type: Prod_3

Description: Product of three influencing factors

Food_Ratio

Type: Gain

Description: Gain factor

Source5

Type: Source

Description: This is the (dummy) source model of System Dynamics

CIAFG

Type: Rate_1

Description: Unrestricted rate element with one influencing variable

CIAF

Type: Reverse_Level

Description: Level of the System Dynamics methodology with time reversal

CIAFD

Type: Rate_1

Description: Unrestricted rate element with one influencing variable

Sink5

Type: Sink

Description: This is the (dummy) sink model of System Dynamics

CIAF_D

Type: Gain

Description: Gain factor

CIAF_G

Type: Gain

Description: Gain factor

Prod_2_3

Type: Prod_2

Description: Product of two influencing factors

P_Abs

Type: Division

Description: Output first input divided by second input

Prod_2_4

Type: Prod_2

Description: Product of two influencing factors

POLCM

Type: Tabular

Description: Tabular function

POLAT

Type: Tabular

Description: Tabular function

CFIFR

Type: Tabular

Description: Tabular function

FPM

Type: Tabular

Description: Tabular function

Prod_2_5

Type: Prod_2

Description: Product of two influencing factors

CIRA

Type: Gain

Description: Gain factor

FPCI

Type: Tabular

Description: Tabular function

CIQR

Type: Tabular

Description: Tabular function

QLMF

Type: Division

Description: Output first input divided by second input

QLM

Type: Tabular

Description: Tabular function

QLF

Type: Tabular

Description: Tabular function

Prod_4_1

Type: Prod_4

Description: Product of four influencing factors

QLC

Type: Tabular

Description: Tabular function

QLP

Type: Tabular

Description: Tabular function

Quality_of_Life

Type: Gain

Description: Gain factor

NR_norm

Type: Parameter_Change

Description: Parameter variation of WORLD2 model

Pol_norm

Type: Parameter_Change

Description: Parameter variation of WORLD2 model

DR_norm

Type: Parameter_Change

Description: Parameter variation of WORLD2 model