Chaotic attractors captured from remote sensing time series for the dynamics of cereal crops

References

• L.A. Aguirre and S.A. Billings, Dynamical effects of overparametrization in nonlinear models, Physica D 80(1–2) (1995), pp. 26–40.
   Google Scholar
• J. Bernussou, L. Hsu, and C. Mira, Quelques exemples du second ordre, Collected Preprints of Colloque International du CNRS, 229, Transformations ponctuelles et applications (Toulouse, September 1973), Proceedings Editions du CNRS (Paris), 1976, pp. 195–226.
   Google Scholar
• L.J. Blanco, J.M. Paruelo, M. Oesterheld, and F.N. Biurrun, Spatial and temporal patterns of herbaceous primary production in semi-arid shrublands: A remote sensing approach, J. Veg. Sci. 27(4) (2016), pp. 716–727.
   Web of Science ®Google Scholar
• E. Bouras, L. Jarlan, S. Khabba, S. Er-Raki, A. Dezetter, F. Sghir, and Y. Tramblay, Assessing the impact of global climate changes on irrigated wheat yields and water requirements in a semi-arid environment of Morocco, Sci. Rep. 9(1) (2019), Article ID 19142.
   Google Scholar
• D. Coca and S.A. Billings, Continuous-time system identification for linear and nonlinear systems using wavelet decompositions, Int. J. Bifur. Chaos 7(1) (1997), pp. 87–96.
   Web of Science ®Google Scholar
• G. Gouesbet and C. Letellier, Global vector field reconstruction by using a multivariate polynomial L2-approximation on nets, Phys. Rev. E 49(6) (1994), pp. 4955–4972.
   Web of Science ®Google Scholar
• F. Grond, H.H. Diebner, S. Sahle, A. Mathias, S. Fischer, and O.E. Rössler, A robust locally interpretable algorithm for Lyapunov exponents, Chaos Solitons Fractals 16(5) (2003), pp. 841–852.
   Web of Science ®Google Scholar
• M. Hénon, A two-dimensional mapping with a strange attractor, Commun. Math. Phys. 50(1) (1976), pp. 69–77.
   Web of Science ®Google Scholar
• B.N. Holben, Characteristics of maximum-value composite images for temporal AVHRR data, Int. J. Remote Sens. 7(11) (1986), pp. 1417–1434.
   Web of Science ®Google Scholar
• L. Jarlan, Y.M. Tourre, E. Mougin, N. Philippon, and P. Mazzega, Dominant patterns of AVHRR NDVI interannual variability over the Sahel and linkages with key climate signals (1982–2003), Geophys. Res. Lett. 32(4) (2005), Article ID L04701.
   Web of Science ®Google Scholar
• L. Jarlan, S. Mangiarotti, E. Mougin, P. Mazzega, and P. Hiernaux, Assimilation of SPOT/VEGETATION NDVI data into a Sahelian vegetation dynamics model, Remote Sens. Environ.112(4) (2008), pp. 1381–1394.
   Web of Science ®Google Scholar
• L. Jarlan, J. Abaoui, B. Duchemin, A. Ouldbba, Y.M. Tourre, S. Khabba, M. Le Page, R. Balaghi, A. Mokssit, and G. Chehbouni, Linkages between common wheat yields and climate in Morocco (1982–2008), Int. J. Biometeorol. 58 (2014), pp. 1489–1502.
   PubMed Web of Science ®Google Scholar
• D.T. Kaplan and L. Glass, Direct test for determinism in a time series, Phys. Rev. Lett. 68(4) (1992), pp. 427–430.
   PubMed Web of Science ®Google Scholar
• J.L. Kaplan and J.A. Yorke, Chaotic behavior of multidimensional difference equations, Lect. Notes Math. 730 (1979), pp. 204–227.
   Google Scholar
• D. Koutsoyiannis, On the quest for chaotic attractors in hydrological processes, Hydrolog. Sci. J. 51(6) (2006), pp. 1065–1091.
   Web of Science ®Google Scholar
• C. Lainscsek, C. Letellier, and I. Gorodnitsky, Global modeling of the Rössler system from the z-variable, Phys. Lett. A 314(5–6) (2003), pp. 409–427.
   Web of Science ®Google Scholar
• W.F. Langford, Numerical studies of torus bifurcations, in International Series of Numerical Mathematics, Vol. 70, 1985, pp. 285–295.
   Google Scholar
• C. Letellier, L. Le Sceller, E. Maréchal, P. Dutertre, B. Maheu, G. Gouesbet, Z. Fei, and J.L. Hudson, Global vector field reconstruction from a chaotic experimental signal in copper electrodissolution, Phys. Rev. E 51(5) (1995), pp. 4262–4266.
   Web of Science ®Google Scholar
• C. Letellier, L.A. Aguirre, and J. Maquet, Relation between observability and differential embeddings for nonlinear dynamics, Phys. Rev. E 71(6) (2005), Article ID 066213.
   Web of Science ®Google Scholar
• C. Letellier, L.A. Aguirre, and U.S. Freitas, Frequently asked questions about global modeling, Chaos: Interdiscip. J Nonlinear Sci. 19(2) (2009), Article ID 023103.
   Web of Science ®Google Scholar
• C. Letellier, R. Abraham, D.L. Shepelyansky, O.E. Rössler, P. Holmes, R. Lozi, L. Glass, A. Pikovsky, L.F. Olsen, I. Tsuda, C. Grebogi, U. Parlitz, R. Gilmore, L.M. Pecora, and T.L. Carroll, Some elements for a history of the dynamical systems theory, Chaos: Interdiscip. J. Nonlinear Sci.31(5) (2021), Article ID 053110. https://doi.org/10.1063/5.0047851.
   Web of Science ®Google Scholar
• E.N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci. 20 (1963), pp. 130–141.
   Web of Science ®Google Scholar
• E.N. Lorenz, Irregularity: A fundamental property of the atmosphere, Tellus 36(A) (1984), pp. 98–110.
   Google Scholar
• R. Lozi, Un attracteur étrange (?) du type attracteur de Hénon, J. Phys. 39(C5) (1978), pp. 9–10.
   Google Scholar
• R. Lozi, Giga-periodic orbits for weakly coupled tent and logistic discretized maps, in Modern Mathematical Models: Methods and Algorithms for Real World Systems, A.H. Siddiqi, I.S. Duff, O. Christensen, eds., Proc. Conf. Intern. on Industrial and Appl. Math., New Delhi, Anamaya, New Delhi, 4–6 Dec. 2004.
   Google Scholar
• J.M. Malasoma, What is the simplest dissipative chaotic jerk equation which is parity invariant?, Phys. Lett. A 264(5) (2000), pp. 383–389.
   Web of Science ®Google Scholar
• J.M. Malasoma, Minimal smooth chaotic flows, in World Scientific Series on Nonlinear Science, Series A, Vol. 84, C. Letellier and R. Gilmore, eds., World Scientific, Singapore, 2013, pp. 281–301.
   Google Scholar
• S. Mangiarotti, Low dimensional chaotic models for the plague epidemic in Bombay (1896–1911), Chaos Solitons Fractals 81 (2015), pp. 184–196.
   Web of Science ®Google Scholar
• S. Mangiarotti and M. Huc, Can the original equations of a dynamical system be retrieved from observational time series?, Chaos: Interdiscip. J Nonlinear Sci. 29(2) (2019), Article ID 023133.
   Web of Science ®Google Scholar
• S. Mangiarotti and C. Letellier, Topological analysis for designing a suspension of the Hénon map, Phys. Lett. A 379(47–48) (2015), pp. 3069–3074.
   Web of Science ®Google Scholar
• S. Mangiarotti and C. Letellier, Topological characterization of toroidal chaos: A branched manifold for the Deng toroidal attractor, Chaos: Interdiscip. J. Nonlinear Sci. 31(1) (2021), Article ID 013129.
   Web of Science ®Google Scholar
• S. Mangiarotti, P. Mazzega, L. Jarlan, E. Mougin, F. Baup, and J. Demarty, Evolutionary bi-objective optimization of a semi-arid vegetation dynamics model with NDVI and 0 satellite data, Remote Sens. Environ. 112(4) (2008), pp. 1365–1380.
   Web of Science ®Google Scholar
• S. Mangiarotti, P. Mazzega, E. Mougin, and P. Hiernaux, The vegetation cycle in West Africa from AVHRR-NDVI data: Horizons of predictability versus spatial scales, Remote Sens. Environ. 114(9) (2010), pp. 2036–2047.
   Web of Science ®Google Scholar
• S. Mangiarotti, R. Coudret, L. Drapeau, and L. Jarlan, Modélisation par approche globale de la dynamique du blé pluvial observée par télédétection spatiale en zone semi-aride, Rencontre Du Non Linéaire 14 (2011), pp. 103–108.
   Google Scholar
• S. Mangiarotti, R. Coudret, L. Drapeau, and L. Jarlan, Polynomial search and global modeling two algorithms for modeling chaos, Phys. Rev. E 86(4) (2012), Article ID 046205.
   Web of Science ®Google Scholar
• S. Mangiarotti, P. Mazzega, P. Hiernaux, and E. Mougin, Predictability of vegetation cycles over the semi-arid region of Gourma (Mali) from forecasts of AVHRR-NDVI signals, Remote Sens. Environ.123 (2012), pp. 246–257.
   Web of Science ®Google Scholar
• S. Mangiarotti, M. Peyre, and M. Huc, A chaotic model for the epidemic of Ebola virus disease in West Africa (2013–2016), Chaos: Interdiscip. J. Nonlinear Sci. 26 (2016), Article ID 113112.
   PubMed Web of Science ®Google Scholar
• S. Mangiarotti, F. Le Jean, M. Huc, and C. Letellier, Global modeling of aggregated and associated chaotic dynamics, Chaos Solitons Fractals 83 (2016), pp. 82–96.
   Web of Science ®Google Scholar
• S. Mangiarotti, Y. Zhang, and M. Leblanc, Chaos theory applied to the modeling of karst springs: First results from univariate time series, Hydrogeol. J. 27(6) (2019), pp. 2027–2043.
   Web of Science ®Google Scholar
• S. Mangiarotti, M. Peyre, Y. Zhang, M. Huc, F. Roger, and Y. Kerr, Chaos theory applied to the outbreak of COVID-19: An ancillary approach to decision-making in pandemic context, Epidemiol. Infect. 148 (2020), Article ID e95.
   PubMed Web of Science ®Google Scholar
• S. Mangiarotti, M. Huc, F. Le Jean, M. Chassan, and L. Drapeau, GPoM (Generalized polynomial modelling), Comprehensive R Archive Network, version 1.3, 2020-02-18. Available at https://CRAN.R-project.org/package=GPoM.
   Google Scholar
• S. Mangiarotti, E. Fu, P. Jouquet, M.T. Tran, M. Huc, and N. Bottinelli, Earthworm activity and its coupling to soil hydrology: A deterministic analysis, Chaos: Interdiscip. J. Nonlinear Sci. 31 (2021), Article ID 013134.
   Web of Science ®Google Scholar
• S. Mangiarotti, L. Drapeau, and C. Letellier, Two chaotic global models for cereal crops cycles observed from satellite in northern Morocco, Chaos: Interdiscip. J. Nonlinear Sci. 24(2) (2021), Article ID 023130.
   Google Scholar
• J. Maquet, C. Letellier, and L.A. Aguirre, Global models from the Canadian lynx cycles as a direct evidence for chaos in real ecosystems, J. Math. Biol. 55(1) (2007), pp. 21–39.
   PubMed Web of Science ®Google Scholar
• N. Martiny, N. Philippon, Y. Richard, C. Camberlin, and C.J.C. Reason, Predictability of NDVI in semi-arid African regions, Theor. Appl. Climatol. 100(3–4) (2010), pp. 467–484.
   Web of Science ®Google Scholar
• R. May, Simple mathematical models with very complicated dynamics, Nature 261(5560) (1976), pp. 45–67.
   Web of Science ®Google Scholar
• P. Mayaux, E. Bartholome, S. Fritz, and A. Belward, A new land-cover map of Africa for the year 2000, J. Biogeogr. 31(6) (2004), pp. 861–877.
   Web of Science ®Google Scholar
• R.B. Myneni and D.L. Williams, On the relationships between FAPAR and NDVI, Remote Sens. Environ. 49(3) (1994), pp. 200–211.
   Web of Science ®Google Scholar
• N. Philippon, N. Martiny, and P. Camberlin, Forecasting the vegetation photosynthetic activity over the Sahel: A model output statistics approach, Int. J. Climatol. 29(10) (2009), pp. 1463–1477.
   Web of Science ®Google Scholar
• H. Poincaré, Les Méthodes Nouvelles De La Mécanique Céleste, Tome iii, Gauthier-Vilard, Paris, 1899.
   Google Scholar
• O.E. Rössler, An equation for continuous chaos, Phys. Lett. A 57(5) (1976), pp. 397–398.
   Web of Science ®Google Scholar
• O.E. Rössler, Chaotic behavior in simple reaction system, Z. Naturforsch. A 31(3–4) (1976), pp. 259–264.
   Google Scholar
• O.E. Rössler, Different types of chaos in two simple differential equations, Z. Naturforsch. A 31(12) (1976), pp. 1664–1670.
   Google Scholar
• O.E. Rössler, An equation for hyperchaos, Phys. Lett. A 71(2–3) (1979), pp. 155–157.
   Web of Science ®Google Scholar
• M. Sáez, S. Mangiarotti, S. Cuezva, A. Fernandezé Cortés, B. Molero, S. Sanchez-Moral, and D. Benavente, Global models for CO2 and 222Rn concentrations in the cave of Altamira, Theor. Appl. Climatol. 143(1–2) (2021), pp. 603–626.
   Web of Science ®Google Scholar
• B. Saltzman, Finite amplitude free convection as an initial value problem – I, J. Atmos. Sci. 19 (1962), pp. 329–341.
   Web of Science ®Google Scholar
• T. Sauer, J.A. Yorke, and M. Casdagli, Embedology, J. Stat. Phys. 65(3–4) (1991), pp. 579–616.
   Web of Science ®Google Scholar
• J.C. Sprott, Some simple chaotic flows, Phys. Rev. E 50(2) (1994), pp. R647–R650.
   PubMed Web of Science ®Google Scholar
• J. Starrett and C. Nicholas, A suspension of the Hénon map by periodic orbits, Chaos Solitons Fractals 45(12) (2012), pp. 1486–1493.
   Web of Science ®Google Scholar
• F. Takens, Detecting strange attractors in turbulence, Lect. Notes Math. 898 (1981), pp. 366–381.
   Google Scholar
• N. Thenon, M. Peyre, M. Huc, A. Touré, F. Roger, and S. Mangiarotti, COVID-19: Underreporting, demographic effect, chaotic dynamics, and mitigation strategy impact, PLoS Negl. Trop. Dis. 16(9) (2022), Article ID e0010735.
   PubMed Web of Science ®Google Scholar
• C.J. Tucker, Satellite remote sensing of total herbaceous biomass production in the Senegalese Sahel: 1980–1984, Remote Sens. Environ. 17(3) (1985), pp. 223–249.
   Web of Science ®Google Scholar
• C.J. Tucker, J.E. Pinzon, M.E. Brown, D.A. Slayback, E.W. Pak, R. Mahoney, E.F. Vermote, and N.E. Saleous, An extended AVHRR 8 km NDVI dataset compatible with MODIS and SPOT vegetation NDVI data, Int. J. Remote Sens. 26(20) (2005), pp. 4485–4498.
   Web of Science ®Google Scholar
• Y. Ueda, The Road to Chaos, Aerial Press, Santa Cruz, CA, 1993.
   Google Scholar
• P.-F. Verhulst, Notice sur la loi que la population suit dans son accroissement, in A. Quetelet, ed., Correspondance mathématique et physique de l'Observatoie de Bruxelles, Ghent, 1838, pp. 113–121.
   Google Scholar