EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 55 (2021) Supplement ESAIM: M2AN, 55 (2021) S653-S675 References
Free Access
Issue
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Page(s) S653 - S675
DOI https://doi.org/10.1051/m2an/2020054
Published online 26 February 2021
  1. C.T. Bauch, R. Sigdel, J. Pharaon and M. Anand, Early warning signals of regime shifts in coupled human–environment systems. Proc. Nat. Acad. Sci. 113 (2016) 14560–14567. [Google Scholar]
  2. D. Burney and T. Flannery, Fifty millennia of catastrophic extinctions after human contact. Trends Ecol. Evol. 20 (2005) 395–401. [PubMed] [Google Scholar]
  3. J.A. Capitán and J.A. Cuesta, Catastrophic regime shifts in model ecological communities are true phase transitions. J. Stat. Mech.: Theory Exp. 2010 (2010, 2010,) P10003. [Google Scholar]
  4. A.A. Cimatoribus, S.S. Drijfhout, V. Livina and G. van der Schrier, Dansgaard-Oeschger events: bifurcation points in the climate system. Clim. Past 9 (2013) 323–333. [Google Scholar]
  5. S. Dai and D.G. Schaeffer, Bifurcations in a modulation equation for alternans in a cardiac fiber. ESAIM: M2AN 44 (2010) 1225–1238. [EDP Sciences] [Google Scholar]
  6. B. deYoung, M. Barange, G. Beaugrand, R. Harris, R.I. Perry, M. Scheffer and F. Werner, Regime shifts in marine ecosystems: detection, prediction and management. Trends Ecol. Evol. 23 (2008) 402–409. [PubMed] [Google Scholar]
  7. A. Dhooge, W. Govaerts, Y.A. Kuznetsov, H.G.E. Meijer and B. Sautois, New features of the software matcont for bifurcation analysis of dynamical systems. Math. Comput. Model. Dyn. Syst. 14 (2008) 147–175. [Google Scholar]
  8. H.A. Dijkstra, Nonlinear Climate Dynamics. Cambridge University Press (2009). [Google Scholar]
  9. H. Engler, H.G. Kaper, T.J. Kaper and T. Vo, Dynamical systems analysis of the Maasch-Saltzman model for glacial cycles. Phys. D: Nonlinear Phenom. 359 (2017) 1–20. [Google Scholar]
  10. H. Fujii, M. Mimura and Y. Nishiura, A picture of the global bifurcation diagram in ecological interacting and diffusing systems. Phys. D: Nonlinear Phenom. 5 (1982) 1–42. [Google Scholar]
  11. P. Gandhi, L. Werner, S. Iams, K. Gowda and M. Silber, A topographic mechanism for arcing of dryland vegetation bands. J. R. Soc. Interface 15 (2018) 20180508. [PubMed] [Google Scholar]
  12. M. Genkai-Kato, Regime shifts: catastrophic responses of ecosystems to human impacts. Ecol. Res. 22 (2006) 214–219. [Google Scholar]
  13. L.J. Gordon, G.D. Peterson and E.M. Bennett, Agricultural modifications of hydrological flows create ecological surprises. Trends Ecol. Evol. 23 (2008) 211–219. [PubMed] [Google Scholar]
  14. N. Hamzah, A. Ross and G. Wake, A bifurcation analysis of a simple phytoplankton and zooplankton model. Math. Comput. Model. 45 (2007) 449–458. [Google Scholar]
  15. K.A. Henderson, C.T. Bauch and M. Anand, Alternative stable states and the sustainability of forests, grasslands, and agriculture. Proc. Nat. Acad. Sci. 113 (2016) 14552–14559. [Google Scholar]
  16. M. Hirota, M. Holmgren, E.H.V. Nes and M. Scheffer, Global resilience of tropical forest and savanna to critical transitions. Science 334 (2011) 232–235. [Google Scholar]
  17. C. Innes, M. Anand and C.T. Bauch, The impact of human–environment interactions on the stability of forest-grassland mosaic ecosystems. Sci. Rep. 3 (2013) 1–10. [Google Scholar]
  18. S.E. Jørgensen, S. Bastianoni, F. Müller, B.C. Patten, B.D. Fath, J.C. Marques, S.N. Nielsen, E. Tiezzi and R.E. Ulanowicz, Ecosystems have complex dynamics – disturbance and decay. In: A New Ecology. Elsevier (2007) 143–166. [Google Scholar]
  19. S. Kéfi, V. Dakos, M. Scheffer, E.H.V. Nes and M. Rietkerk, Early warning signals also precede non-catastrophic transitions. Oikos 122 (2012) 641–648. [Google Scholar]
  20. B. Kooi, Numerical bifurcation analysis of ecosystems in a spatially homogeneous environment. Acta Biotheor. 51 (2003) 189–222. [CrossRef] [PubMed] [Google Scholar]
  21. S.A. Levin, Ecosystems and the biosphere as complex adaptive systems. Ecosystems 1 (1998) 431–436. [Google Scholar]
  22. S.D. Ling, C.R. Johnson, S.D. Frusher and K.R. Ridgway, Overfishing reduces resilience of kelp beds to climate-driven catastrophic phase shift. Proc. Nat. Acad. Sci. 106 (2009) 22341–22345. [Google Scholar]
  23. P.V. Martn, J.A. Bonachela, S.A. Levin and M.A. Muñoz, Eluding catastrophic shifts. Proc. Nat. Acad. Sci. 112 (2015) E1828–E1836. [Google Scholar]
  24. M. Meyries, J.D.M. Rademacher and E. Siero, Quasi-linear parabolic reaction-diffusion systems: a user’s guide to well-posedness, spectra, and stability of travelling waves. SIAM J. Appl. Dyn. Syst. 13 (2014) 249–275. [Google Scholar]
  25. A. Neishtadt, On stability loss delay for dynamical bifurcations. Disc. Contin. Dyn. Syst. - S 2 (2009) 897–909. [Google Scholar]
  26. M. Rietkerk, Self-organized patchiness and catastrophic shifts in ecosystems. Science 305 (2004) 1926–1929. [Google Scholar]
  27. L. Russo, K. Spiliotis, F. Giannino, S. Mazzoleni and C. Siettos, Bautin bifurcations in a forest-grassland ecosystem with human–environment interactions. Sci. Rep. 9 (2019) 1–8. [CrossRef] [PubMed] [Google Scholar]
  28. M. Scheffer, Foreseeing tipping points. Nature 467 (2010) 411–412. [PubMed] [Google Scholar]
  29. M. Scheffer and E. Jeppesen, Regime shifts in shallow lakes. Ecosystems 10 (2007) 1–3. [Google Scholar]
  30. M. Scheffer, S. Carpenter, J.A. Foley, C. Folke and B. Walker, Catastrophic shifts in ecosystems. Nature 413 (2001) 591–596. [CrossRef] [PubMed] [Google Scholar]
  31. R. Seydel, Practical Bifurcation and Stability Analysis. Springer, New York (2010). [Google Scholar]
  32. E. Siero, A. Doelman, M.B. Eppinga, J.D.M. Rademacher, M. Rietkerk and K. Siteur, Striped pattern selection by advective reaction-diffusion systems: resilience of banded vegetation on slopes. Chaos: Interdiscip. J. Nonlinear Sci. 25 (2015) 036411. [Google Scholar]
  33. K. Siteur, M.B. Eppinga, A. Doelman, E. Siero and M. Rietkerk, Ecosystems off track: rate-induced critical transitions in ecological models. Oikos 125 (2016) 1689–1699. [Google Scholar]
  34. K. Spiliotis, L. Russo, F. Giannino, S. Cuomo, C. Siettos and G. Toraldo, Nonlinear Galerkin methods for a system of PDEs with Turing instabilities. Calcolo 55 (2018) 9. [Google Scholar]
  35. A.C. Staver, S. Archibald and S.A. Levin, The global extent and determinants of savanna and forest as alternative biome states. Science 334 (2011) 230–232. [Google Scholar]
  36. T. Troost, B. Kooi and S. Kooijman, Bifurcation analysis of ecological and evolutionary processes in ecosystems. Ecol. Model. 204 (2007) 253–268. [CrossRef] [Google Scholar]
  37. H. Yu, M. Zhao and R.P. Agarwal, Stability and dynamics analysis of time delayed eutrophication ecological model based upon the Zeya reservoir. Math. Comput. Simul. 97 (2014) 53–67. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you