Multivariate recurrence plots for visualizing and quantifying the dynamics of spatially extended ecosystems

Ecological Complexity

Volumn 6, Issue 1, 2009, Pages 37-47

  Proulx, Raphaël ^a   Côté, Pascal ^a   Parrott, Lael ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Characteristic length scale; Nonlinear dynamics; Recurrence quantification analysis; Sensor network; Spatiotemporal complexity; Textural discontinuity

Indexed keywords

EID: 58349117416     PISSN: 1476945X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ecocom.2008.10.003     Document Type: Article

References (40)

1. Broomhead D.S., and King G.P. Extracting qualitative dynamics from experimental data. Physica D 20 (1986) 217-236
2. Casdagli M.C. Recurrence plots revisited. Physica D 108 (1997) 12-44
3. Dennis B., Desharnais R.A., Cushing J.M., Henson S.M., and Costantino R.F. Can noise induce chaos?. Oikos 102 (2003) 229-239
4. Eckmann J.-P., Kamphorts S.O., and Ruelle D. Recurrence plots of dynamical systems. Europhysics Letters 4 (1987) 973-977
5. Egolf D.A., and Greenside H.S. Relation between fractal dimension and spatial correlation length for extensive chaos. Nature 369 (1994) 129-131
6. Ellner S.P., and Turchin P. When can noise induce chaos and why does it matter, a critique. Oikos 111 (2005) 620-631
7. Faure P., and Korn H. A new method to estimate the Kolmogorov-Sinai entropy from recurrence plots, its application to neuronal signals. Physica D 122 (1998) 265-279
8. Godfray H.C., and Blythe S.P. Complex dynamics in multispecies communities. Philosophical Transactions of the Royal Society of London B 330 (1990) 221-233
9. Grassberger P., and Procaccia I. Characterization of strange attractors. Physical Review Letters 50 (1983) 346-349
10. Habeeb R.L., Johnson C.R., Wotherspoon S., and Mumby P.J. Optimal scales to observe habitat dynamics, a coral reef example. Ecological Applications 17 (2007) 641-647
11. Hastings A., Hom C.L., Ellner S., Turchin P., and Godfray C.H. Chaos in ecology, is mother nature a strange attractor?. Annual Review in Ecology and Systematics 24 (1993) 1-33
12. Hilborn R.C. Chaos and nonlinear dynamics. An Introduction for Scientists and Engineers (2000), Oxford University Press, NY (Chapter 10)
13. Holling C.S. Cross-scale morphology, geometry, and dynamics of ecosystems. Ecological Monographs 62 (1992) 447-502
14. Kurths J., Romano M.C., Thiel M., Osipov G.V., Ivanchenko M.V., Kiss I.Z., and Hudson J.L. Synchronization analysis of coupled noncoherent oscillators. Nonlinear Dynamics 44 (2006) 135-149
15. March T.K., Chapman S.C., and Dendy R.O. Recurrence plot statistics and the effect of embedding. Physica D 200 (2005) 171-184
16. Marwan, N., Saparin, P., Kurths, J., 2005. Generalisation of recurrence plot analysis for spatial data. International Symposium on Nonlinear Theory and its Applications. NOLTA2005, Bruges, pp. 630-633.
17. Marwan N., Wessel N., Meyerfeldt U., Schirdewan A., and Kurths J. Recurrence-plot-based measures of complexity and their application to heart-rate-variability data. Physical Review E 66 (2002) 026702
18. Montgomery R.A. Effects of understory foliage and patterns of light attenuation near the forest floor. Biotropica 36 (2004) 33-39
19. Parrott L. Analysis of simulated long-term ecosystem dynamics using visual recurrence analysis. Ecological Complexity 1 (2004) 111-125
20. Pascual M., and Levin S. From individuals to population densities, searching for the intermediate scale of nontrivial determinism. Ecology 80 (1999) 2225-2236
21. Proulx R., and Parrott L. Measures of structural complexity in digital images for monitoring the ecological signature of an old-growth forest ecosystem. Ecological Indicators 8 (2008) 270-284
22. Rand D.A., and Wilson H.B. Using spatio-temporal chaos and intermediate-scale determinism to quantify extended ecosystems. Proceedings of the Royal Society of London B 259 (1995) 111-117
23. Riley M.A., Balasubramaniam R., and Turvey M.T. Recurrence quantification analysis of postural fluctuations. Gait and Posture 9 (1999) 65-78
24. Romano M.C., Thiel M., Kurths J., and von Bloh W. Multivariate recurrence plots. Physics Letters A 330 (2004) 214-223
25. Smith, A.R., 1978. Color gamut transform pairs. In: Beatty J.C., Booth K.S. (Eds.), Tutorial, Computer Graphics, second ed., 1982 IEEE Computer Society Press, Silver Spring, pp. 376-383.
26. Solé R.V., and Bascompte J. Self-organisation in Complex Ecosystems (2006), Princeton University Press, Princeton
27. Stark J. Observing complexity, seeing simplicity. Philosophical Transactions of the Royal Society of London A 358 (2000) 41-61
28. Takens F. Detecting strange attractors in turbulence. In: Rand D., and Young L.-S. (Eds). Dynamical Systems and Turbulence (1981), Springer Lecture Notes in Mathematics, Berlin 366-381
29. Thiel M., Romano M.C., Kurths J., Meucci R., Allaria E., and Arecchi F.T. Influence of observational noise on the recurrence quantification analysis. Physica D 171 (2002) 138-152
30. Thiel M., Romano M.C., and Kurths J. Analytical description of recurrence plots of white noise and chaotic processes. Applied Nonlinear Dynamics 11 (2003) 20-29
31. Thiel M., Romano M.C., Read P.L., and Kurths J. Estimation of dynamical invariants without embedding by recurrence plots. Chaos 14 (2004) 234-243
32. Trulla L.L., Giuliani A., Zbilut J.P., and Webber Jr. C.L. Recurrence quantification analysis of the logistic equation with transients. Physics Letters A 223 (1996) 255-260
33. Vasconcelos D.B., Lopes S.R., Viana R.L., and Kurths J. Spatial recurrence plots. Physical Review E 73 (2006) 056207
34. von Bloh W., Romano M.C., and Thiel M. Long-term predictability of mean daily temperature data. Nonlinear Processes in Geophysics 12 (2005) 471-479
35. Wardlow B.D., and Egber S.L. Large-area crop mapping using time-series MODIS 250m NDVI data: an assessment for the US. Central Great Plains. Remote Sensing of Environment 112 (2008) 1096-1116
36. Webber Jr. C.L., and Zbilut J.P. Dynamical assessment of physiological systems and states using recurrence plot strategies. Journal of Applied Physiology 76 (1994) 965-973
37. Zbilut J.P., and Webber Jr. C.L. Embeddings and delays as derived from quantification of recurrence plots. Physics Letters A 171 (1992) 199-203
38. Zbilut J.P., Giuliani A., and Webber Jr. C.L. Recurrence quantification analysis as an empirical test to distinguish relatively short deterministic versus random number series. Physics Letters A 267 (2000) 174-178
39. Zbilut J.P., Thomasson N., and Webber Jr. C.L. Recurrence quantification analysis as a tool for nonlinear exploration of nonstationary cardiac signals. Medical Engineering and Physics 24 (2002) 53-60
40. Zoldi S.M., and Greenside H.S. Karhunen-Loève decomposition of extensive chaos. Physical Review Letters 78 (1997) 1687-1690