反恐措施与经济增长：一个微分对策王臥王鹏2|长春工业大学理学院，长春市1300122吉林大学数学学院，长春市130012摘要：在本文中，我们考虑了在一个合理的方式下如何分配政府的有限资源才能有利于经济的发展和国防的稳定。在确定情形和随机情形下，我们分别给出了相应的微分対策，同吋还分析了恐怖分子的攻击同经济发展的关系。对不同突发爭件造成的不同影响进行了模拟。关键词：随机微分对策；鞍点；反恐措施：O225Q211.63Counterterrormeasuresandeconomicgrowth:AdifferentialgameWANGJum,WANGPengz1SchoolofBasicScience,ChangChunUniversityOfTechnology,Changchun1300122CollegeofMathematics,激linUniversity,Changchun130012Abstract:Inthispaper,weconsiderhowtoallotthegovernment'slimitedresourcesinareasonablewaythatwillbenefiteconomicdevelopmentanddefenseterroristorganizationssimultaneously.Thesaddlepointsofdeterministicandstochasticdifferentialgamesweregiven.TherelationshipbetweenteiToristattackandeconomicdevelopmentwasanalyzed.Thedifferencesofstrategiescausedbyunexpectedeventsareshown・Keywords:stochasticdifferentialgames;saddlepoint;counterterrormeasures.0IntroductionTherampantterrorismisagrowingproblemthroughouttheworld.Torootupallterroristorganizationsisonlyafantasyforthetimebeing・Attacksendangernationalsecurityanddisrupteconomicdevelopment,sohowtokeepawayfromterroristattacksandimprovenationaldefensehasalreadybecomethefocalproblemthatattractsworldwideattentionandpopulartopic.DuetothehostilitybetweenthegovernmentandtheteiToristorganizations,theoptimalcontrolmethodandgametheoryareusuallyadoptedtostudyterroristattacksandrelevant11:SpecializedResearchFundfortheDoctoralProgramofHigherEducation(2009(X)6112(X)38)作者简介：WangJun(1982-)•Female,lecturer^majorresearchdirection：differentialgames.Conespondenceauthor：WangPeng(1977・),male>associateprofessor•majorresearchdirection：thenumericalanalysisofstochasticdifferentialequations.model[1,2,3,4,5,6,7]・Theimpactofterroristattacksoneconomycannotbeignored[9」()]・Differentperformanceindicesareusedtodescribeeconomicchanges,suchaspublicopinions[10].However,economicchangesalsodeterminethecounterterrormeasures,whichfurtherimpactterrorism.Therefore,differentialgameswereusedinthispapertostudytherelationshipbetweenterroristattacksandeconomicdevelopment.Terroristattackshavedifferenttypes,suchasinvasion,assassinationandthecontrolofpublicopinion,allofwhichdemandcorrespondingpersonnel,technology,weapons,andfunding.Allabovecanbegenerallycalledresourcesofterroristorganization(RTO),that'swhatthegovernmentsaretryingtoweakenasanimportantpartofcountertenortask[2,4]-ThispartofourmodelisrelatedtoRef.[4],whichdiscussedstate-separabilityofgames・Ontheotherhand,steadyeconomicdevelopmentisthegovernments^chiefduty.Furthermore,asiswell-knownthecounterterrorcapacityisdecidedbythegovernments,economicstrength.Therefore,counterterrormeasuremodelsshouldnotonlyconsiderRTObutalsoeconomicdevelopment.Thus,thispaperfocusesoncounterterrormeasuresandeconomicdevelopmentcomprehensively,whichwerenotdiscussedinpreviouscountertenormodels・Wediscusshowtoallotthegovernments9limitedresourcesinareasonableway.Also,therelatioshipbetweenterroristattackandeconomicdevelopmentisshown.1ModelandDefinitionWeconsideradeterministicdifferentialgameinthissection.Therearetwostatefunctionsx(f)andy(/),wherex(t)describesRTOstock,includingpersonnel,technology,capital,andweaponsetc.,andy(t)describesthegovernment’sresources,thati...