Restricted accessResearch articleFirst published online 2016-2
Edward N Lorenz’s 1963 paper,“Deterministic nonperiodic flow”,in Journal of the Atmospheric Sciences,Vol 20,pages 130–141: Its history and relevance to physical geography
Lorenz (1963) provided the foundation of chaos theory and inspired a fundamental reappraisal of systems’ nonlinearity in many disciplines, including physical geography. I will provide a brief overview of chaos in nonlinear systems as documented in Lorenz (1963), including the major tenants of chaos theory, followed by a discussion of the effects of chaos theory within meteorology and climate sciences, geomorphology, and ecology and biogeography. In general, Lorenz (1963) provided the intellectual framework for reconsidering the predictability of many physical systems.
AllenJCSchafferWMRoskoD (1993) Chaos reduces species extinction by amplifying local population noise. Nature364: 229–231.
2.
CavalieriLFKoçakH (1994) Chaos in biological control systems. Journal of Theoretical Biology169: 179–187.
3.
CavalieriLFKoçakH (1995) Intermittent transition between order and chaos in an insect pest population. Journal of Theoretical Biology175: 231–234.
4.
ChurchM (1996) Space, time, and the mountain: how do we order what we see? In: RhodesBLThornCE (eds) The Scientific Nature of Geomorphology: Proceedings of the 27th Binghamton Symposium in Geomorphology, 27–29 September, 1996, 147–170. West Sussex: John Wiley & Sons.
5.
CullingWEH (1987) Equifinality: modern approaches to dynamical systems and their potential for geographical thought. Transactions of the Institute of British Geographers12: 57–72.
6.
DavisWM (1899) The geographical cycle. The Geographical Journal14: 478–504.
7.
DeAngelisDLWaterhouseJC (1987) Equilibrium and nonequilibrium concepts in ecological models. Ecological Monographs57: 1–21.
8.
EarnDJRohaniPGrenfellBT (1998) Persistence, chaos, and synchrony in ecology and epidemiology. Proceedings of the Royal Society of London B: Biological Sciences265: 7–10.
9.
GleickJ (1997) Chaos: Making a New Science. New York: Random House.
10.
LorenzEN (1963) Deterministic nonperiodic flow. Journal of the Atmospheric Sciences20: 130–141.
11.
LorenzEN (1972) Predictability: does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?Paper presented at the 139th meeting of the American Association for the Advancement of Science, Washington DC. Available at: http://eaps4.mit.edu/research/Lorenz/Butterfly_1972.pdf.
12.
LorenzEN (1995) The Essence of Chaos. Seattle: University of Washington Press.
13.
MalansonGP (1997) Effects of feedbacks and seed rain on ecotone patterns. Landscape Ecology12: 27–38.
14.
MalansonGP (1999) Considering complexity. Annals of the Association of American Geographers89: 746–753.
15.
MalansonGPButlerDRWalshSJ (1990) Chaos theory in physical geography. Physical Geography11: 293–304.
16.
MalansonGPButlerDRGeorgakakosKP (1992) Nonequilibrium geomorphic processes and deterministic chaos. Geomorphology5: 311–322.
17.
MalansonGPScuderiLMoserKA. (2014) The composite nature of physical geography: moving from linkages to integration. Progress in Physical Geography38: 3–18.
18.
MayRM (1974) Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science186: 645–647.
19.
MayRM (1976) Simple mathematical models with very complicated dynamics. Nature261: 459–467.
20.
OsterkampWRHuppCR (1996) The evolution of geomorphology, ecology, and other composite sciences. In: RhodesBLThornCE (eds) The Scientific Nature of Geomorphology: Proceedings of the 27th Binghamton Symposium in Geomorphology, 27–29 September, 1996, 416–441. West Sussex: John Wiley & Sons.
21.
PalmerTN (2009) Edward Norton Lorenz. 23 May 1917–16 April 2008. Biographical Memoirs of Fellows of the Royal Society55: 139–155.
22.
PattenBC (1997) Synthesis of chaos and sustainability in a nonstationary linear dynamic model of the American black bear (Ursus americanus Pallas) in the Adirondack Mountains of New York. Ecological Modelling100(1): 11–42.
23.
PhillipsJD (1992) Nonlinear dynamical systems in geomorphology: revolution or evolution?Geomorphology5: 219–229.
24.
PhillipsJD (1993a) Instability and chaos in hillslope evolution. American Journal of Science293: 25–48.
25.
PhillipsJD (1993b) Spatial-domain chaos in landscapes. Geographical Analysis25: 101–117.
26.
PhillipsJD (1995) Nonlinear dynamics and the evolution of relief. Geomorphology14: 57–64.
27.
PhillipsJD (1996) Deterministic complexity, explanation, and predictability in geomorphic systems. In: RhodesBLThornCE (eds) The Scientific Nature of Geomorphology: Proceedings of the 27th Binghamton Symposium in Geomorphology, 27–29 September, 1996, 315–335. West Sussex: John Wiley & Sons.
28.
PhillipsJD (1999a) Divergence, convergence, and self-organization in landscapes. Annals of the Association of American Geographers89(3): 466–488.
29.
PhillipsJD (1999b) Spatial analysis in physical geography and the challenge of deterministic uncertainty. Geographical Analysis31(4): 359–372.
30.
QinSJiaoJJWangS (2002) A nonlinear dynamical model of landslide evolution. Geomorphology43(1): 77–85.
31.
QinSJiaoJJWangS. (2001) A nonlinear catastrophe model of instability of planar-slip slope and chaotic dynamical mechanisms of its evolutionary process. International Journal of Solids and Structures38(44): 8093–8109.
32.
RenwickWH (1992) Equilibrium, disequilibrium and nonequilibrium landforms in the landscape. Geomorphology5: 265–276.
33.
RoulstoneINorburyJ (2013) Invisible in the Storm: the role of mathematics in understanding weather. Princeton, NJ: Princeton University Press.
34.
SchafferWMKotM (1986) Chaos in ecological systems: the coals that Newcastle forgot. Trends in Ecology & Evolution1(3): 58–63.
35.
ShuklaJ (1998) Predictability in the midst of chaos: a scientific basis for climate forecasting. Science282(5389): 728–731.
36.
Smith-McKennaEKMalansonGPReslerLM., (2014) Cascading effects of feedbacks, disease, and climate change on alpine treeline dynamics. Environmental Modelling & Software62: 85–96.
37.
SuárezI (1999) Mastering chaos in ecology. Ecological Modelling117(2): 305–314.
38.
TothZKalnayE (1993) Ensemble forecasting at NMC: the generation of perturbations. Bulletin of the American Meteorological Society74: 2317–2330.
39.
TothZKalnayE (1997) Ensemble forecasting at NCEP and the breeding method. Monthly Weather Review125: 3297–3319.
