Wonderland model (Ofer Abarbanel online library)

Wonderland is an integrated mathematical model used for studying phenomena in sustainable development. First introduced by economist (Waren C. Sanderson 1994) of Stony Brook University, there are now several related versions of the model in use. Wonderland allows economists, policy analysts and environmentalist to study the interactions between the economic, demographic and anthropogenic sectors of an idealized world, thereby enabling them to obtain insights transferable to the real world.


Wonderland is a compact model. In total, there are only four continuous state variables, one each for the economic and demographic sectors and two for the anthropogenic sector; thus making Wonderland more compact and amenable to analysis than larger, more intricate models like World3. For this reason it is often used as an initial testing ground for new techniques in the area of policy analysis (Lempert, et al., 2003).

System behavior

Using the Scenario analysis technique, Sanderson (1994) studied two possible futures for the idealized world described by Wonderland. One future entitled Dream, held out the possibility of unending sustainable growth, while the other termed Horror, ended in environmental collapse and eventual extinction of the population. Subsequent work (Kohring, 2006) showed that the parameters of the model can be bisected into two sets, one which always produces sustainable futures and one which always ends in collapse and extinction. Additionally, the equations of Wonderland exhibit chaotic behavior (Gröller, et al., 1996, Wegenkittl, et al., 1997, Leeves and Herbert, 1998).


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  • Gröller, E.; Wegenkittl, R.; Milik, A; Prskawetz, A.; Feichtinger, G.; Sanderson, W.C. (1996). “The geometry of wonderland”. Chaos, Solitons & Fractals. 7: 1989–2006. Bibcode:1996CSF…..7.1989G. doi:10.1016/s0960-0779(96)00067-7.
  • Herbert, R.D.; Leeves, G. D. (1998). “Troubles in Wonderland”. Complexity International. 6: 1–20.
  • Herbert, R.D.; Bell, R.D.; Leeves, G. D.; Lewis, B.G. (December 12–15, 2005). “Economic and Environmental Impacts of Pollution Control in a Multi-Country Model.”. In Zerger, A.; Argent, R.M. (eds.). MODSIM05 Proceedings. MODSIM2005. pp. 1035–1041.
  • Kohring, G.A (2006). “Avoiding Chaos in Wonderland”. Physica A. 368: 214–224. arXiv:nlin/0602028. Bibcode:2006PhyA..368..214K. doi:10.1016/j.physa.2006.01.061.
  • Leeves, G. D.; Herbert, R.D. (2002). “Economic and environmental impacts of pollution control in a system of environment and economic interdependence”. Chaos, Solitons & Fractals. 13: 693–700. Bibcode:2002CSF….13..693L. doi:10.1016/s0960-0779(01)00003-0.
  • Lempert, R.J.; Popper, S.W.; Bankes, S.C. (2003). Shaping the Next One Hundred Years: New Methods for Quantitative, Long-Term Policy Analysis. Santa Monica: Rand.
  • Sanderson, W.C. (1994), “Simulation Models of Demographic, Economic, and Environmental Interactions”, in Lutz, W. (ed.), Population, Development, Environment: Understanding Their Interactions in Mauritius, Berlin: Springer, pp. 33–71
  • Wegenkittl, R.; Grõller, E.; Purgathofer, W. (1997). “Visualizing the Dynamical Behavior of Wonderland”. IEEE Computer Graphics and Applications. 17: 71–79. doi:10.1109/38.626972.

Ofer Abarbanel – Executive Profile

Ofer Abarbanel online library

Ofer Abarbanel online library

Ofer Abarbanel online library