Diffusion-driven instabilities and emerging spatial patterns in patchy landscapes
Tài liệu tham khảo
Bekker, 2009, Landscape metrics indicate differences in patterns and dominant controls of ribbon forests in the Rocky Mountains, USA, Appl. Veg. Sci., 12, 237, 10.1111/j.1654-109X.2009.01021.x
Benson, 1993, Analysis of pattern formation in reaction diffusion models with spatially inhomogeneous coefficients, Math. Comput. Modelling, 17, 29, 10.1016/0895-7177(93)90025-T
Benson, 1998, Unravelling the Turing bifurcation using spatially varying diffusion, J. Math. Biol., 37, 318, 10.1007/s002850050135
Benson, 1993, Diffusion driven instability in an inhomogeneous domain, Bull. Math. Biol., 55, 365, 10.1007/BF02460888
Bonachela, 2015, Termite mounds can increase the robustness of dryland ecosystems to climatic change, Science, 347, 651, 10.1126/science.1261487
Botsford, 2001, Dependence of sustainability on the configuration of marine reserves and larval dispersal distance, Ecol. Lett., 4, 144, 10.1046/j.1461-0248.2001.00208.x
Cantrell, 2012, The implications of model formulation when transitioning from spatial to landscape ecology, Math. Biosci., 9, 27, 10.3934/mbe.2012.9.27
Deblauwe, 2008, The global biogeography of semi-arid periodic vegetation, Global Ecol. Biogeogr., 17, 715, 10.1111/j.1466-8238.2008.00413.x
Doedel, 1981, Auto, a program for the automatic bifurcation analysis of autonomous systems, Cong. Numer., 30, 265
Doedel, 2006, Numerical continuation of branch points of equilibria and periodic orbits, 145
Doedel, 1991, Numerical analysis and control of bifurcation problems: (i) Bifurcation in finite dimensions, Int. J. Bifurc. Chaos, 1, 493, 10.1142/S0218127491000397
Eppinga, 2009, Nutrients and hydrology indicate the driving mechanisms of peatland surface patterning, Am. Nat., 173, 803, 10.1086/598487
Ergon, 2001, Life-history traits of voles in a fluctuating population respond to the immediate environment, Nature, 411, 1043, 10.1038/35082553
Fasani, 2011, Factors promoting or inhibiting Turing instability in spatially extended prey–predator systems, Ecol. Model., 222, 3449, 10.1016/j.ecolmodel.2011.07.002
Formosa-Jordan, 2012, Regulation of neuronal differentiation at the neurogenic wavefront, Development, 139, 2321, 10.1242/dev.076406
Garzón-Alvarado, 2012, Numerical tests on pattern formation in 2D heterogeneous mediums: an approach using the Schnakenberg model, Dyna, 79, 56
Gasull, 1997, Limit cycles in the Holling–Tanner model, Publ. Mat., 41, 149, 10.5565/PUBLMAT_41197_09
Gierer, 1972, A theory of biological pattern formation, Kybernetik, 12, 30, 10.1007/BF00289234
Gilbert, 1994
Gouhier, 2010, Ecological processes can synchronise marine population dynamics over continental scales, Proc. Natl. Acad. Sci. U. S. A., 107, 8281, 10.1073/pnas.0914588107
Horsthemke, 2004, Turing instability in inhomogeneous arrays of diffusively coupled reactors, J. Phys. Chem. A, 108, 2225, 10.1021/jp037029k
Jones, 2006, Intercroppping sunflower in organic vegetables to augment bird predators of arthropods, Agric. Ecosys. Environ., 117, 171, 10.1016/j.agee.2006.03.026
Leroux, 2013, Mechanistic models for the spatial spread of species under climate change, Ecol. Appl., 23, 815, 10.1890/12-1407.1
Liu, 2013, Phase separation explains a new class of self-organized spatial patterns in ecological systems, Proc. Natl. Acad. Sci. U. S. A., 110, 11905, 10.1073/pnas.1222339110
Lubensky, 2011, A dynamical model of ommatidial crystal formation, Proc. Natl. Acad. Sci. U. S. A., 108, 11145, 10.1073/pnas.1015302108
May, 1974
Meron, 2012, Pattern-formation approach to modelling spatially extended ecosystems, Ecol. Model., 234, 70, 10.1016/j.ecolmodel.2011.05.035
Mukhopadhyay, 2006, Modeling the role of diffusion coefficients on Turing instability in a reaction–diffusion predator–prey system, Bull. Math. Biol., 68, 293, 10.1007/s11538-005-9007-2
Murray, 2001
O’Dea, 2011, Multiscape analysis of pattern formation via intercellular signalling, Math. Biosci., 231, 172, 10.1016/j.mbs.2011.03.003
O’Dea, 2013, The isolation of spatial patterning modes in a mathematical model of juxtacrine cell signalling, Math. Med. Biol., 30, 95, 10.1093/imammb/dqr028
Okubo, 2001
Owen, 1998, Mathematical modelling of juxtacrine cell signalling, Math. Biosci., 153, 125, 10.1016/S0025-5564(98)10034-2
Owen, 2000, Lateral induction by juxtacrine signaling is a new mechanism for pattern formation, Dev. Biol., 217, 54, 10.1006/dbio.1999.9536
Page, 2003, Pattern formation in spatially heterogeneous Turing reaction–diffusion models, Physica D, 181, 80, 10.1016/S0167-2789(03)00068-X
Page, 2005, Complex pattern formation in reaction–diffusion systems with spatially varying parameters, Physica D, 202, 95, 10.1016/j.physd.2005.01.022
Perumpanani, 1995, Phase differences in reaction–diffusion–advection systems and applications to morphogenesis, IMA J. Appl. Math., 55, 19, 10.1093/imamat/55.1.19
Petrovskii, 2001, Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics, Theor. Popul. Biol., 59, 157, 10.1006/tpbi.2000.1509
Rietkerk, 2002, Self-organisation of vegetation in arid ecosystems, Am. Nat., 160, 524, 10.1086/342078
Rietkerk, 2008, Regular pattern formation in real ecosystems, Trends Ecol. Evol., 23, 169, 10.1016/j.tree.2007.10.013
Rietkerk, 2004, Self-organized patchiness and catastrophic shifts in ecosystems, Science, 305, 1926, 10.1126/science.1101867
Sato, 1993, Modeling of wave regeneration in subalpine Abies forests: population dynamics with spatial structure, Ecology, 74, 1538, 10.2307/1940081
Schmitz, 2010, Spatial dynamics and ecosystem functioning, PLOS Biol., 8, e1000378, 10.1371/journal.pbio.1000378
Segel, 1972, Dissipative structure: an explanation and an ecological example, J. Theor. Biol., 37, 545, 10.1016/0022-5193(72)90090-2
Sheffer, 2013, Emerged or imposed: a theory on the role of physical templates and self-organisation for vegetation patchiness, Ecol. Lett., 127–139, 16
Sherratt, 2013, History-dependent patterns of whole ecosystems, Ecol. Complex., 14, 8, 10.1016/j.ecocom.2012.12.002
Sherratt, 2015, Using wavelength and slope to infer the historical origin of semi-arid vegetation bands, Proc. Natl. Acad. Sci. U. S. A., 112, 4202, 10.1073/pnas.1420171112
Sherratt, 2002, Generation of periodic waves by landscape features in cyclic predator–prey systems, Proc. R. Soc. Lond. B, 269, 327, 10.1098/rspb.2001.1890
Sherratt, 1995, Ecological chaos in the wake of invasion, Proc. Natl. Acad. Sci. U. S. A., 92, 2524, 10.1073/pnas.92.7.2524
Siero, 2015, Striped pattern selection by advective reaction–diffusion systems: resilience of banded vegetation on slopes, Chaos, 25, 036411, 10.1063/1.4914450
Siteur, 2014, Beyond Turing: the response of patterned ecosystems to environmental change, Ecol. Complex., 20, 81, 10.1016/j.ecocom.2014.09.002
Spencer, 1995, A simple predator–prey model of exploited marine fish populations incorporating alternative prey, ICES J. Marine Sci., 53, 615, 10.1006/jmsc.1996.0082
Strohm, 2009, The effect of habitat fragmentation on cyclic population dynamics: a numerical study, Bull. Math. Biol., 71, 1323, 10.1007/s11538-009-9403-0
Turchin, 2001
van der Stelt, 2013, Rise and fall of periodic patterns for a generalized Klausmeier–Gray–Scott model, J. Nonlinear Sci., 23, 39, 10.1007/s00332-012-9139-0
Voroney, 1996, Turing pattern formation in heterogeneous media, Physica D, 99, 303, 10.1016/S0167-2789(96)00132-7
Wang, 2010, Nonlinear dynamic and pattern bifurcations in a model for spatial patterns in young mussel beds, J. R. Soc. Interface, 6, 705, 10.1098/rsif.2008.0439
Wang, 2010, Pattern formation of a predator–prey system with Ivlev-type functional response, Ecol. Model., 221, 131, 10.1016/j.ecolmodel.2009.09.011
Wearing, 2000, Mathematical modelling of juxtacrine patterning, Bull. Math. Biol., 62, 293, 10.1006/bulm.1999.0152
Wearing, 2001, Nonlinear analysis of juxtacrine patterns, SIAM J. Appl. Math., 62, 283, 10.1137/S003613990037220X
Webb, 2004, Intra-membrane ligand diffusion and cell shape modulate juxtacrine patterning, J. Theor. Biol., 230, 99, 10.1016/j.jtbi.2004.04.024
Webb, 2004, Oscillations and patterns in spatially discrete models for developmental intercellular signalling, J. Math. Biol., 48, 444, 10.1007/s00285-003-0247-1
Weerman, 2012, Changes in diatom patch-size distribution and degradation in a spatially self-organized intertidal mudflat ecosystem, Ecology, 93, 608, 10.1890/11-0625.1
Wolfrum, 2012, The Turing bifurcation in network systems: collective patterns and single differentiated nodes, Physica D, 241, 1351, 10.1016/j.physd.2012.05.002
Yizhaq, 2014, Effects of heterogeneous soil–water diffusivity on vegetation pattern formation, Water Resour. Res., 50, 5743, 10.1002/2014WR015362
Zelnik, 2015, Gradual regime shifts in fairy circles, Proc. Natl. Acad. Sci. U. S. A., 10.1073/pnas.1504289112