简介：Inthispaper,weinvestigatethestationaryprobabilitydistributionandmeanfirstpassagetimeinavegetationecologicalsystem,whichisdrivenbycross-correlationbetweenintrinsicandextrinsiccolorednoisesaswellasthenonzerocross-correlationinbetween.Theimpactsoftheself-correlationtimeτ1andτ2,thecross-correlationtimeτ3andintensitykonthestationaryprobabilitydistributionandmeanfirstpassagetimearediscussed,respectively.Ourmainresultsshowthat:(i)theself-correlationtimeτ1caninduceregimeshiftsfromthedesertstatetothesustainablevegetationstate,whiletheself-correlationtimeτ2,cross-correlationtimeτ3andintensitykcaninduceregimeshiftsfromthesustainablevegetationstatetothedesertstate;and(ii)theself-correlationtimeτ1orτ2canenhancethestabilityofthesustainablevegetationbiomass,whilethecross-correlationtimeτ3orstrengthkweakensthestabilityofthesustainablevegetationbiomass.

简介：Ithasbeenreportedthattheminimalspatiallyextendedphytoplankton-zooplanktonsystemexhibitsbothtemporalregular/chaoticbehaviour,andspatiotemporalchaosinapatchyenvironment.Asafurtherinvestigationbymeansofcomputersimulationsandtheoreticalanalysis,inthispaperweobservethatthespiralwavesmayexistandthespatiotemporalchaosemergewhentheparametersarewithinthemixedTuring-Hopfbifurcationregion,whicharisesfromthefar-fieldbreakupofthespiralwavesoveralargerangeofdiffusioncoefficientsofphytoplanktonandzooplankton.Moreover,thespatiotemporalchaosarisingfromthefar-fieldbreakupofspiralwavesdoesnotgraduallyinvadethewholespaceofthatregion.Ourresultsareconfirmedbynonlinearbifurcationofwavetrains.Wealsodiscussecologicalimplicationsofthesespatiallystructuredpatterns.