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1、NonlinearAnalysis39(2000)483{497Optimizationproblemsforone-impulsivemodelsfrompopulationdynamics1J.Angelova,A.DishlievDepartmentofMathematics,UniversityofChemicalTechnologyandMetallurgy,bull.KlimentOhridsky8,Soa1756,BulgariaReceived29September1997;accepted13January1998Keywords:Impulsivemoment;Im

2、pulsivemodel;Populationdynamics;Impulsivelogistic;Gompertzmodels1.IntroductionImpulsivedierentialequations(IDE)aresuitablemathematicalmodelsforalargeclassofrealprocesses.Theseprocessesaresubmittedtoshorttemporaryperturbations,thatarenegligiblecomparedtotheprocessduration.Thustheperturbationsoccur

3、mmediately"asimpulses.TherstresultsinthetheoryofIDEhavebeenreportedfromV.Mil'manandA.Myshkis[6,7].Basicmonographsonthissubjectare[1{5,9].TheIDEarewidelyappliedin:experimentalphysics,chemistry,biology,engineering,andpopulationdynamics.InthispaperusingIDEsomeoptimizationproblemsfrompopulationdynami

4、csforisolatedpopulationaresolved.Thepopulationisconsideredtobeisolated,ifthereisneitherimmigrationnoremigration.Mostofmodelsofsinglespeciesdynamicshavebeenderivedfromthedierentialequation(DE)dN(t)=f(t;N);(1)dtwhereN=N(t)>0isthepopulationbiomass(size)intimet0;f(t;N)and1=Nf(t;N)aretotalandspecicg

5、rowthratesofthepopulationbiomass(fortheiso-latedpopulationthefunction1=Nf(t;N)iscalledaccommodationfunction).Correspondingauthor.Tel.:0035926254535;fax:003592685488;e-mail:dana@adm1.uctm.acad.bg1ThisresearchhasbeenpartiallysupportedbyBulgarianMinistryofEducation,ScienceandTechnologiesundergrantMM

6、511.0362-546X/99/$-seefrontmatter?1999ElsevierScienceLtd.Allrightsreserved.PII:S0362-546X(98)00216-8484J.Angelova,A.Dishliev/NonlinearAnalysis39(2000)483{497Iff(t;N)=f(N)thereisatemporalconstancyoftheenvironment(stationaryen-vironment).Variouschoicesofftogetherwithsomeecologicalassumptionsaboutthe

7、environmentleadtovariousDEmodels.Forexample,iff(t;N)=r=KN(K−N)weobtainthelogisticDEdNr=N(K−N);(2)dtKwhereK=K(t)>0isthecapacityofenvironment(saturationlevel);r=r(t)>0isthereproductivepotentialofpopulation.Iff(t;N)