WOLFRAM SYSTEMMODELER

Scenario_5

5th Scenario

Diagram

Wolfram Language

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Click for copyable input
SystemModel["SystemDynamics.WorldDynamics.World2.Scenario_5"]
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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.


Public 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