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非自治时滞反馈控制系统的周期解分岔和混沌 总被引:9,自引:0,他引:9
研究时滞反馈控制对具有周期外激励非线性系统复杂性的影响机理,研究对应的线性平衡态失稳的临界边界,将时滞非线性控制方程化为泛函微分方程,给出由Hopf分岔产生的周期解的解析形式.通过分析周期解的稳定性得到周期解的失稳区域,使用数值分析观察到时滞在该区域可以导致系统出现倍周期运动、锁相运动、概周期运动和混沌运动以及两条通向混沌的道路:倍周期分岔和环面破裂.其结果表明,时滞在控制系统中可以作为控制和产生系统的复杂运动的控制“开关”. 相似文献
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Effects of time delayed velocity feedbacks on self-sustained oscillator with excitation 总被引:1,自引:0,他引:1
Both the primary resonant solutions and their bifurcations due to time delayed velocity feedbacks used in a self-sustained oscillator with excitation were further investigated. A model was proposed by adding linear and nonlinear time delayed feedbacks to a representative non- autonomous system ( with external forcing ). The stability condition of the linearized system at trivial equilibrium was discussed, which leads to a critical stability boundary where periodic solutions may occur. The main attention was focused on bifurcations from the primary resonant solutions. It is found that the stable primary resonant solution may appear periodically in the time delay. Meanwhile, the unstable regions for such solutions are also obtained, predicting the occurrence of quasi-periodic motions. 相似文献
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非线性系统的长期规则运动除了平衡点和周期解以外,概周期解,或有时表现为拟周期解也是一种长期规则运动。无论是在理论上,还是在实际计算中,确定概周期解这种规则运动远比前二者困难。本文用简单胞映射方法结合一定的技巧,数值计算周期非线性系统的概周期解。 相似文献
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本文对具有自动频率跟踪和反馈稳幅功能的电磁振动机械进行了研究.对实现电子闭环控制的一个半自由度非线性动力学系统(见图1)建立了一个三维机、电振动微分方程纽。应用中心流形定理和Normal Form定理对这类具有自激振动性质的方程组求得第一次近似解.又以GZJ—4型机为例,计算了定常解的稳定域,并给出定常解同电磁铁激磁电压之间的关系.对设计和调试这类产品有指导意义. 相似文献
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求解非线性振动问题的一种新方法 总被引:1,自引:0,他引:1
首先把描述非线性振动的微分方程归结为一非线性积分微分方程,然后把此积分微分方程的求解转化为一无穷阶的非线性代数方程组的求解。从理论上讲,可得到满足任何精度要求的周期解。本文用此方法对Dufing系统进行了分析。 相似文献
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1 IntroductionandtheProblemPresentedSeekingtheexplicitsolutionofthenonlinearpartialdifferentialequation (NPDEs)isanimportantsubjectinsolitontheoryanditsapplication .Formanyyears,themainattentionwaspaidtotheconstantcoefficientNPDEs[1~ 7],manypowerfulmethodshavebeenproposedanddeveloped.Inrecentyears,moreandmoreattentionshavebeenpaidtovariablecoefficientNPDEs[8~ 13].Manymethodssuchassimilarityreductionmethod ,truncatedexpansionmethodandhomogeneousbalancemethodhavebeenextendedtosolvevaria… 相似文献
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In this paper, the new forms of the differential equations of motion of the systems with higher-order nonholonomic constraints are obtained at first, and then the equivalence between these equations and the known equations is demonstrated. Finally an example is given to illustrate the application of our new equations. 相似文献
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IntroductionLetC(k- 1)2π =h(t) |h :R →Ris (k -1 )_thordercontinuousdifferentiableandh(t+ 2π) ≡h(t) , C2π =h(t) |h :R →Riscontinuousandh(t+ 2π) ≡h(t) , ‖h(t)‖ =supt∈ [0 ,2π] |h(t) | , ‖h(t)‖Pk- 1 =max‖h(t)‖ ,‖h′(t)‖ ,… ,‖h(k- 1) (t)‖ , x(m) (t+ ·) (θ) =x(m) (t+θ) θ∈R (m =0 ,1 ,2 ,… ,k-1 ) .Clearly ,x(m) (t + ·) ∈C2π, … 相似文献
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王志华 《应用数学和力学(英文版)》1999,20(3):328-331
IntroductionInrecenttenyears,becauseoftheneedofthecontroltheoryandeconomics,thetheoryofdifferentialinclusionshasbeendevelopingfast,andsome~tresultSindifferenhalinclusionshavebeenobtained.Asystematicstudyondifferenhalinclusionscanbefoundin[l].Inordertosuitcontroltheory,thefollowingsendlineardifferentialinclusionswereconsideredin[2~4]:x'(t) Ax(t)6F(t,x(t)),a.e.teI,x(0)=xo'(l)xthereAgeneratesalinearsendgroup(compactorequicolltinuouS),XisasepotleBanachspaCe,I=[0,TiisanintervalofR,F:IxX~Zx\0i… 相似文献
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房辉 《应用数学和力学(英文版)》2000,21(3):291-296
1 ProblemintheResearchofToroidImpulsivedifferentialequationisanewimportantbranchofdifferentialequation.In1989,[1],[2]systematicallysummarizedresearchworkaboutimpulsiveordinarydifferentialequations.Inrecentyears,therearemanyliteraturesdealingwiththeoscillatio… 相似文献
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This paper studies existence of at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, by using the Green function and maximum principle, existence of solutions of a nonlinear telegraph system is equivalent to existence of fixed points of an operator. By imposing growth conditions on the nonlinearities, existence of at least three fixed points in cone is obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces. In other words, there exist at least three positive doubly periodic solutions of nonlinear telegraph system. 相似文献
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THEEXISTENCEOFPERIODICSOLUTIONSFORACLASSOFFUNCTIONALDIFFERENTIALEQUATIONSANDTHEIRAPPLICATIONZhaoJie-min(赵杰民);HuangKe-lei(黄克累)... 相似文献
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Huang Nanjing 《应用数学和力学(英文版)》1997,18(6):599-603
In this paper, a new kind of generalized BBM equation is introduced and discussed. Some existence theorems of periodic traveling
wave solutions for this kind generalized BBM equation are given. 相似文献
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A class of implicit fuzzy differential inclusions(IFDIs) are introduced and studied.Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed situation,respectively.A viable solution for a closed IFDI is proved to exist under the tangential condition.As an application,an implicit fuzzy differential equation,which comes from the drilling dynamics in petroleum engineering,is analyzed numerically.The obtained results can improve and extend some known results for fuzzy differential inclusions(FDIs) and fuzzy differential equations(FDEs),which might be helpful in the analysis of fuzzy dynamic systems. 相似文献
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宋福民 《应用数学和力学(英文版)》1998,19(11):1103-1113
I.IntroductionOwingtothefactthatthesystemwithwhicheconomics,biologyandsoonaredefinitelyconcernedtohaveuncertainty,includingthatcausedbyrestrictiononknowledge.asformathematicaltreatment,generallytheycanonlybedescribedbymeansofdifferentialinclusionsinsteadofdifferentialequations.Itiswell-knownthatthederivativex')ofasolutionx.)tothedifferentialequationx'(t)=f(t,x(t))inheritsthereqularityproperitiesofthemapfandthefunctionx(').Thisisnolongerthecasewithdifferentialinclusionsandisoneofthereasonswhyt… 相似文献
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IntroductionandProblemintheResearchofToroidThispaperdealswiththeexistenceof2π_periodicsolutionstothenonlinearsystemoffirst_orderdifferentialequationswithadeviatingargument x(t) =Bx(t) F(x(t-τ) ) p(t) ,( 1 )wherex(t)∈R2 , x(t) =ddtx(t) ,τ∈R ,B∈R2×2 ,F :R2 →R2 isboundedandp∈C(… 相似文献