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1、MATHEMATICALMODELSOFVEGETATIONPATTERNFORMATIONINECOHYDROLOGY1211F.Borgogno,P.D’Odorico,F.Laio,andL.RidolfiReceived13November2007;accepted24October2008;published18March2009.[1]Highlyorganizedvegetationpatternscanbefoundinathesystem,leadingtotheemergenceofsta
2、blenumberoflandscapesaroundtheworld.Inrecentyears,heterogeneousconfigurations.Bothdeterministicandseveralauthorshaveinvestigatedtheprocessesunderlyingstochasticmechanismsmayexplaintheself-organizedvegetationpatternformation.Patternsthatareinducedvegetationp
3、atternsobservedinnature.Afteranextensiveneitherbyheterogeneityinsoilpropertiesnorbythelocalanalysisofdeterministictheories,wereviewnoise-inducedtopographyaregenerallyexplainedastheresultofspatialmechanismsofpatternformationandprovidesomeself-organizationres
4、ultingfrom‘‘symmetry-breakingexamplesofapplicationsrelevanttotheenvironmentalinstability’’innonlinearsystems.Inthiscase,thespatialsciences.dynamicsareabletodestabilizethehomogeneousstateofCitation:Borgogno,F.,P.D’Odorico,F.Laio,andL.Ridolfi(2009),Mathematic
5、almodelsofvegetationpatternformationinecohydrology,Rev.Geophys.,47,RG1005,doi:10.1029/2007RG000256.becamevisiblewiththeadventofaerialphotographyEcohydrologyisthescience,whichseekstodescribethehydrologic[e.g.,Macfadyen,1950b].Figures1–4showsomeexam-mechanism
6、sthatunderlieecologicpatternsandprocesses.plesofspectacularspatiallyperiodicvegetationpatternsthat[Rodriguez-Iturbe,2000,p.3]canbefoundespeciallyinaridandsemiaridlandscapesaroundtheworld.Thesepatternsexhibitamazingregular1.INTRODUCTIONconfigurationsofvegeta
7、tionstripesorspotsseparatedbybaregroundareas.Insomecases,patternsmayspreadover[2]Inmanylandscapesaroundtheworldthevegetationrelativelylargeareas(uptoseveralsquarekilometers)coverissparseandexhibitsspectacularorganizedspatial[White,1971;Eddyetal.,1999;Valent
8、inetal.,1999;features[e.g.,Macfadyen,1950b]thatcanbeeitherspatiallyEstebanandFairen,2006]andcanbefoundondifferentperiodicorrandom.Commonlydenotedas‘‘vegetationsoilsandwithabroadvarietyofvegetationspeci
