简介：Theauthorsinvestigatetheglobalpropertiesofgeneralautonomoussystemsontheplaneandestablishcriteriaforthenonexistence,existenceanduniquenessoflimitcycles.Asapplicationexamples,thelimitcyclesforsomepolynomialsystemsarestudied.

简介：<正>Inthispaperwegivethenecessaryandsufficientconditionsforallfinitecriticalpointsofquadraticdifferentialsystemstobeweakfoci,andsolveanopenproblemproposedbyYanqianYe.

简介：LetFF_vbethesetoffaultynodesinann-dimensionalfoldedhypercubeFQ_nwith|FF_v|≤n-1andallfaultyverticesarenotadjacenttothesamevertex.Inthispaper,weshowthatifn≥4,theneveryedgeofFQn-FF_vliesonafault-freecycleofeveryevenlengthfrom6to2~n-2|FF_v|.

简介：一张标记的图是订的对(G，L)由图G和它的标记的L组成：V(G)鈫?{1，2，鈥？n}，在此n=|V(G)|。在一张标记的图的一条增加的nonconsecutive路径(G，L)任何一个是一条路径(u1，u2，鈥？uk)(k鈮?2)在G以便L(ui)+为所有i=的2鈮?L(ui+1)1，2，鈥？k？1或顺序1的一条路径。增加nonconsecutive路径在的全部的数字(G，L)被d表示(G，L)。如果标记的L生产最大的d，标记的L是最佳的(G，L)。在这份报纸，在Zverovich(2004)的比那简单的一个方法被给获得路径的最佳的标记。象周期和星那样的另外的特殊的图的最佳的标记被获得。

简介：这份报纸的目的是描绘谁的世袭代数学的首先分级的Hochschildcohomology加布里埃尔发抖被承认有面向的周期。我们获得了的有趣的结论证明首先分级的Hochschildcohomology的标准基础取决于类一是的quiver一个拓扑的目标。在这份报纸，我们为在哪儿的世袭代数学克服古典Hochschildcohomology的限制加布里埃尔发抖被假定非循环。作为准备，我们首先在路径代数学和联系分级的谎言代数学上调查分级的微分操作员。

简介：Thispaperinvestigatesthepredator-preysystem:x=k1（x-ax）-k（x）y,y=(-k3+βk（x）ywit.k（x）=k2x,x≤x,k2x,x>τ,whereα,β,τ;k1,k2,k3arepositiveconstants.Themainresultsareasfollows（i）Incasek3-βk2τ≥0system（1）hasnolimitcycle.（ii）Incasek3-βk2τ<0,k1+k3-βk2τ>0,andforO<α<<1,system（1）atleasthastwolimitcycles.

简介：InthispaperweprovethatifTisaregularn-partitetournamentwithn≥>6,theneacharcofTliesonak-cyclefork=4,5,…,n.OurresultgeneralizestheoremsduetoAlspachandGuorespectively.

简介：Inthispaper,HamiltoniancyclesanddecompositionsofCayleydigraphsareinvestigat-ed.Sufficientconditionsaregivenforthesetwoproblemsrespectively.Furthermore,theconditionsarealsonecesaaryfor2-regularCayleydisraphs,Inaddition,someknownresultsabouttheCartesianproductsoftwodirectedcyclesarealsodeduced.

简介：在这份报纸，我们为间隔地图与某旋转对介绍强烈简单的周期的观点并且证明如果一张间隔地图与给定的旋转对有一个周期，那么，它与一样的旋转对有一个强烈简单的周期。关键词间隔地图-强烈简单的周期-旋转对先生(2000)题目分类58F10-54H20工程由NNSF支持了(10461001，10361001)并且GNSF(0447004)

简介：Aclassofquarticandquinticdifferentialsystemisintroduced.Weshowthatundersuitableassumptions,one,twoorfouralgebraiclimitcyclescanoccur.Theselimitcyclesareanalyticallygiven.

简介：UsingtheaveragingtheoryoffirstandsecondorderwestudythemaximumnumberoflimitcyclesofgeneralizedLinarddifferentialsystems{x=y+εhl1（x）+ε2hl2（x）,y=-x-ε(fn1（x）y2p+1+gm1（x）)+∈2(fn2（x）y2p+1+gm2（x）),whichbifurcatefromtheperiodicorbitsofthelinearcenterx=y,y=-x,whereεisasmallparameter.Thepolynomialshl1andhl2havedegreel;fn1andfn2havedegreen;andgm1,gm2havedegreem.p∈Nand[·]denotestheintegerpartfunction.

简介：Inthispaper,weinvestigatethenumber,locationandstabilityoflimitcyclesinaclassofperturbedpolynomialsystemswith(2n+1)or(2n+2)-degreebyconstructingdetectionfunctionandusingqualitativeanalysis.Weshowthatthereareatmostnlimitcyclesintheperturbedpolynomialsystem,whichissimilartotheresultofPerkoin[8]byusingMelnikovmethod.Forn=2,weestablishthegeneralconditionsdependingonpolynomial'scoefficientsforthebifurcationlocationandstabilityoflimitcycles.Thebifurcationparametervalueoflimitcyclesin[5]isalsoimprovedbyus.Whenn=3thesufficientandnecessaryconditionsfortheappearanceof3limitcyclesaregiven.Twonumericalexamplesforthelocationandstabilityoflimitcyclesareusedtodemonstrateourtheoreticalresults.

简介：在这份报纸，我们证明没有邻近的短周期的2-degenerate图和一些平面图是有大尺寸和最大的度的-edge-choosable,和一些平面图是的组((G)+1)组(G)-edge-choosable。

简介：ForagraphG,wedenotebyp(G)andc(G)thenumberofverticesofalongestpathandalongestcycleinG,respectively.ForavertexvinG,id(v)denotestheimplicitdegreeofv.Inthispaper,weobtainthatifGisa2-connectedgraphonnverticessuchthattheimplicitdegreesumofanythreeindependentverticesisatleastn+1,theneitherGcontainsahamiltonianpath,orc(G)≥p(G)-1.

简介：Abstract.Itisprovedthatthequadraticsystemwithaweakfocusandastrongfocushasatmostonelimitcyclearoundthestrongfocus,andastheweakfocusisa2nd-order(or3rd-order)weakfocusthequadraticsystemhasatmosttwo(one)limitcycleswhichhave(1,1)-distribution((0,1)-distribution).

简介：Inthispaper,wefocusonthevertex-fault-tolerantcyclesembeddingonenhancedhypercube,whichisanattractivevariantofhypercubeandisobtainedbyaddingsomecomplementaryedgesfromhypercube.LetFvbethesetoffaultyverticesinthen-dimensionalenhancedhypercubeQn,k（1≤k≤n-1）.When|Fv|=2,weshowedthatQn,k-Fvcontainsafault-freecycleofeveryevenlengthfrom4to2n-4wheren（n≥3）andfchavethesameparity;andcontainsafault-freecycleofeveryevenlengthfrom4to2n-4,simultaneously,containsacycleofeveryoddlengthfromn—fc+2to2n-3wheren（≥3）andfchavethedifferentparity.Furthermore,when|Fv|=fv≤n-2,weproofthatthereexiststhelongestfault-freecycle,whichisofevenlength2n-2fvwhethern（n>3）andfehavethesameparityornot;andthereexiststhelongestfault-freecycle,whichisofoddlength2n-2fv-1inQn,k—Fvwheren（≥3）andfchavethedifferentparity.

简介：1.IntroductionWeconsideranextensivesystemofthefamiliarLotka-Volterrasysteminwhichthepopulationshaveself-inhibit(i.e.,withtheadditionofdampingterm)thatcanbemodeledbytheequationswherexandyrepresentthepreydensityandpredatordensityrespectively.Thespecifi...

简介：Inthispaper,bifurcationofsmallamplitudelimitcyclesfromthedegenerateequilibriumofathree-dimensionalsystemisinvestigated.Firstly,themethodtocalculatethefocalvaluesatnilpotentcriticalpointoncentermanifoldisdiscussed.Thenanexampleisstudied,bycomputingthequasi-Lyapunovconstants,theexistenceofatleast4limitcyclesonthecentermanifoldisproved.Intermsofdegeneratesingularityinhigh-dimensionalsystems,ourworkisnew.

简介：让G是有最大的度的一张平面图。在这份报纸，如果任何4周期不邻近为任何i的i周期，我们证明那{3，4}在G，那么色彩的数字xl(G)=和表总计的表边色彩的数字xl(G)=+1。

简介：