共查询到20条相似文献,搜索用时 31 毫秒
1.
Consideringsystem:x=φ(y)-F(x),y=-g(x){(E)inwhichF(x)=∫x0f(t)dt,f(x),g(x),φ(y)arecontinuous,andsatisfytheconditionswhichensur... 相似文献
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THE VARIATION OF INVARIANT LINES AND LIMIT CYCLES FOR A QUADRATIC DIFFERENTIAL SYSTEM 总被引:1,自引:0,他引:1
1IntroductionConsidertherealquadraticdiferentialsystemx=-y+δx-4x2+3xy+13y2y=x(1-13x-y).(1)First,forconvenience,wedenotethetwo... 相似文献
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Ye Weiyin 《数学年刊B辑(英文版)》1998,19(3):359-368
§1.Forthesystemx=-y+δx+lx2+ny2=P(x,y),y=x(1+ax-y)=Q(x,y),{(1.1)wecanfindin[1]thefolowing:ConjectureI.Assume1a<0,n>1,n+l>0,na2... 相似文献
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Asiswel-knownwhenarealquadraticdiferentialsystem:x=-y+δx+lx2+mxy+ny2=P(x,y),y=x(1+ax+by)=Q(x,y)(1)hasfourfinitecriticalpoints... 相似文献
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§1. IntroductionByaBCI-algebrawemeananalgebra(X,,0)oftype(2,0)withthefollowingcondi-tions:(1)((xy)(xz))(zy)=0;(2)(x(xy))y=0;(3)xx=0;(4)xy=yx=0impliesx=y.IfaBCI-algebra(X,,0)satisfies(5)0x=0.thenitiscalledaBCK-algebra.InaBCI-algebra,thef… 相似文献
6.
王现 《Annals of Differential Equations》1998,(2)
Bytranslatingandscaling,anygeneralrealcubicLienardsystemsx=y-(α0+α1x+α2x2+α3x3),y=-(β0+β1x+β2x2+β3x3),canbechangedintox=y-(δx... 相似文献
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1IntroductionConsiderathirdordernonlinearcontrolsystemintheformx…+F(r)x¨+G(r)x·+H(r)x=e(t),(1)whereF(r)=1-ε[1+kn(ε)r2],G(r)=1... 相似文献
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1IntroductionThesocaledVolterapradator-preymodelwithundercrowdingefect[1]isasystemintheformofx=ax(x-L)(k-x)-bxy,y=-cy+dxy-αy2... 相似文献
9.
Consideraplanarperturbedsystemoftheformx=Hy+εf(x,y),y=-Hx+εg(x,y)(1)whereH,f,garefunctionsofclasC∞.Asumeforε=0(1)tohaveahomoc... 相似文献
10.
ByaBCI-algebrawemeananalgebra(X;,0)oftype(2,0)satisfyingtheaxioms:(1)((xy)(xz))(zy)=0;(2)(x(xy))y=0;(3)xx=0;(4)xy=yx=0x=yforanyx,yandzinX.ForanyBCI-algebraX,therelation≤definedbyx≤yifandonlyifxy=0isapartialorderonX[1].InanyBCI-algebraX,… 相似文献
11.
THE MATHEMATICAL BEHAVIOR OF A NONAUTONOMOUS VOLTERRA PREDATOR-PREY SYSTEM WITH UNDERCROWDING EFFECT
1IntroductionWeconsidertheVolterapredatorpreymodelwithLogisticpreygrowthrate:x=ax(K-x)-bxy,y=-cy+dxy-αy2.(1.1)Thismodelhasau... 相似文献
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§1.IntroductionConsiderthefolowingddimensionalVlasovPoisonsystem,d=2,3,tf+v·xf-E·vf=0,f(0,x,v)=f0(x,v),E(t,x)=c(d)∫x-y|x... 相似文献
14.
1IntroductionandResultsConsiderthequadraticsystem[1]dxdt=-y+δx+lx2+mxy+ny2=P2(x,y),dydt=x(1+ax+by)=Q2(x,y),(n≥0,ab≠0)E2withou... 相似文献
15.
Riccati微分方程的可积条件 总被引:6,自引:1,他引:5
In1998,ZhaoLinlong[1]obtainedtheintegrablecondition:R=1αγPe2∫(Q-βD)dx (α,β,γisconst).(1)ForRiccatiequation:y′=p(x)y2+Q(x)y+R(x) (PR≠0).(2) Herethenewintegrableconditionsisgiven:L[y0]=1αγPe2∫(Q+2y0p-βD)dx.(3)L[AB+y0]=1αγ(AB)2L[y0]e2∫(2BAL[y0]+Q+2y… 相似文献
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Byfolowingmechanism:AaαX,CcαY,B+XbαY+D,X+Yeα3Y,YfαF,XλαF,article[1]obtainedthefolowingsystem:x=a-bx-exy2-λx,y=bx+exy2-fy+c.(1... 相似文献
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陶有山 《数学物理学报(A辑)》1995,15(2):168-171
本文讨论Goursat问题:{□u≡utt-uxx-uyy=F(t,x,y,u),(t,x,y)∈Γ:x^2+y^2〈tu│эΓ=0设F(t,x,y,u)关于各个变量充分光滑。以光维Γ内的完备切边算子系tээx+xээx+yээy,tээx+xээt,tээy+yээt,xээy-yээx为生成元所生成的切向量场记为Z,由Z构造余法型空间I^k,1。将线性Goursat问题转化成Cauchy问题, 相似文献
18.
函数f(x)在区间[a,b]上单调增加(或单调减少),又c、d∈[a,b]上,若f(c)=f(a),则有c=d.1 求代数式的值例1 已知x、y∈[-π4,π4],a∈R,且 x3+sinx-2a=04y3+sinycosy+a=0则cos(x+2y)= .(1994年全国高中数学竞赛题)解 由已知条件,可得 x3+sinx=2a(-2y)3+sin(-2y)=2a故可设函数f(t)=t3+sint,则有f(x)=f(-2y)=2a.由于函数f(t)=t3+sint,在[-π2,π2]上是单… 相似文献
19.
Liu Deming 《东北数学》1999,(2)
§1.IntroductionForthefolowingpolynomialsystemofdegreem:dxdt=f1(x,y),dydt=f2(x,y),(E)wheref1(x,y)andf2(x,y)arepolynomialsinxan... 相似文献
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1IntroductionandtheResultConsideraplanaranalyticsystemoftheformx=P(x,y),y=Q(x,y),(1.1)wherePandQareanalyticfunctionsin(x,y)in... 相似文献