登录 | 注册 | 充值 | 退出 | 公司首页 | 繁体中文 | 满意度调查
综合馆
具有同宿轨的系统在扰动下的分岔及混沌行为
参考文献
  • [1] Battelli F;Palmer K J. Tangcncies between stable and unstable manifolds. Proc Roy Soc Edin, 1992
  • [2] Fe(c)kan M. Bifurcation from degenerate homoclinics in periodically forced systems. {H}DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 1999
  • [3] Gruendler J. Homoclionic solutions for autonomous systems in arbitrary dimension. {H}SIAM Journal on Mathematical Analysis, 1992
  • [4] Gruendler J. Homoclinic solutions for autonomous ordinary differential equations with nonautonomous perturbations. {H}Journal of Differential Equations, 1995
  • [5] Gruendler J. The existence of transversal homoclinic solutions for higher order equations. {H}Journal of Differential Equations, 1996
  • [6] Hale J K;Lin X B. Heteroclinic orbits for retarded functional differential equations. {H}Journal of Differential Equations, 1986
  • [7] Luo G;Zhu C. Transversal homoclinic orbits and chaos for functional differential equations. Nonlinear Anal:TMA, 2009
  • [8] Battelli F;Lazzari C. Exponential dichotomies,heteroclinic orbits,and Melnikov functions. {H}Journal of Differential Equations, 1990
  • [9] Hale J K. Bifurcation theory and applications. {H}Berlin:Springer-Verlag, 1984
  • [10] Chow S N;Hale J K;Mallet-Paret J. An example of bifurcation to homoclinic orbits. {H}Journal of Differential Equations, 1980
  • [11] Hale J K. Ordinary Differcntial Equations. {H}New York:Wiley-Interscience, 1969
  • [12] Zhu C;Luo G;Shu Y. The existences of transverse homoclinic solutions and chaos for parabolic equations. {H}Journal of Mathematical Analysis and Applications, 2007
  • [13] Guckenheimer J;Holmes P. Nonlinear Oscillations,Dynamical Systems,and Bifurcations of Vector Fields. {H}New York:Springer-Verlag, 1983
  • [14] Hale J K;Spezamiglio A. Perturbation of homoclinics and subharmonics in Duffing' s equation. Nonlinear Anal:TMA, 1985
  • [15] Battelli F;Pahner K J. Chaos in the Duffing equation. {H}Journal of Differential Equations, 1993
  • [16] Chow S N;Hale J K. Methods of Bifurcation Theory. {H}New York:Springer-Verlag, 1982
  • [17] Knobloch J. Bifurcation of degenerate homoclinic orbits in reversible and conservative systems. J Dyn Diff Eqns, 1997
  • [18] He Z;Zhang W. Subharmonic bifurcations in a perturbed nonlinear oscillation. Nonlinear Anal:TMA, 2005
  • [19] Freddy D;Li C;Zhang Z. Unfolding of a quadratic integrable system with two centers and two unbounded heteroclinic loops. {H}Journal of Differential Equations, 1997
  • [20] Gan S;Wen L. Heteroclinic cycles and homoclinic closures for generic diffeomorphisms. J Dyn Diff Eqns, 2003
  • [21] Zeng W. Exponential dichotomies and transversal homoclinic orbits in degenerate cases. J Dyn Diff Eqns, 1995
  • [22] Han M;Hu S;Liu X. On the stability of double homoclinic and heteroclinic cycles. Nonlinear Anal:TMA, 2003
  • [23] Li W;Lu K. Sternberg theorems for random dynamical systems. {H}Communications on Pure and Applied Mathematics, 2005
  • [24] Lin X. Using Melnikov' s method to solve Silnikov' s problem. Proc Roy Soc Edin, 1990
  • [25] Lin X;Vivancos I B. Heteroclinic and periodic cycles in a perturbed convection model. {H}Journal of Differential Equations, 2002
  • [26] Liu B;Zanolin F. Boundedness of solutions of nonlinear differeutial equations. {H}Journal of Differential Equations, 1998
  • [27] Luo G;Liang J;Zhu C. The transversal homoclinic solutions and chaos for stochastic ordinary differential equations. {H}Journal of Mathematical Analysis and Applications, 2013
  • [28] Palmer K J. Exponential dichotomies for almost periodic equation. {H}Proceedings of the American Mathematical Society, 1987
  • [29] Palmer K J;Stoffer D. Chaos in almost periodic systems. {H}ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1989
  • [30] Palmer K J. Existence of transversal homoclinic points in a degenerate case. {H}Rocky Mountain Journal of Mathematics, 1990
  • [31] Wiggins S. Global bifurcations and chaos-analytical methods. {H}New York:Springer-Verlag, 1988
  • [32] Zhu C. The coexistence of subharmonics bifurcated from homoclinic orbits in singular systems. {H}NONLINEARITY, 2008
  • [33] Bulsara A R;Schieve W C;Jacobs E W. Homoclinic chaos in systems perturbed by weak Langevin noise. {H}Physical Review, 1990
  • [34] Deng G;Zhu D. Homoclinic and heteroclinic orbits for near-integrable coupled nonlinear Schr(o)dinger equations. Nonlinear Analysis:TMA, 2010
  • [35] Melnikov V K. On the stability of the center for time periodic perturbations. Trans Moscow Math Soc, 1963
  • [36] Neimark J I;Silnikov L P. A case of generation of periodic motions. Soviet Math Docl, 1965
  • [37] Palmer K J. Exponential dichotomies and transversal homoclinic points. {H}Journal of Differential Equations, 1984
  • [38] Silnikov L P. A case of the existence of a countable number of periodic motions. {H}Soviet Math Dokl, 1965
  • [39] Silnikov L P. On a Poincaré-Birkhoff problem. Math USSR-Sb, 1967
  • [40] Awrejcewicz J;Holicke M M. Smooth and Nonsmooth High Dimensional Chaos and the Melnikov-Type Methods. {H}Singapore:World Scientific, 2007
  • [41] Zhu C;Zhang W. Linearly independent homoclinic bifurcations parameterized by a small function. {H}Journal of Differential Equations, 2007
  • [42] Zhu C;Luo G;Lan K. Multiple homoclinic solutions for singular differential equations. Ann Inst H Poincare:AN, 2010
  • [43] Arnold L. Random Dynamical Systems. {H}New York:Springer-Verlag, 1998
  • [44] Jaeger L;Kantz H. Homoclinic tangencies and non-normal Jacobians-effects of noise in nonhyperbolic chaotic systems. Physica, 1997
  • [45] Kennedy J;York J. Topological horseshoes. {H}Transactions of the American Mathematical Socity, 2001
  • [46] Zhang W. Bifurcation of homoclinics in a nonlinear oscillation. Acta Math Sinica:Engl, 1989
  • [47] Deng B. The bifurcations of countable connections from a twisted heteroclinic loop. {H}SIAM Journal on Mathematical Analysis, 1991
  • [48] Holmes P;Marsden J. Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom. {H}COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1981
  • [49] Lu K;Wang Q. Chaos in differential equations driven by a nonautonomous force. {H}NONLINEARITY, 2010
  • [50] Palmer K J. Transversal heteroclinic orbits and Cherry' s example of a non-integrable hemiltonian system. {H}Journal of Differential Equations, 1986
  • [51] Lu K;Wang Q. Chaos behavior in differential equations driven by a Brownian motion. {H}Journal of Differential Equations, 2011
  • [52] Chow S N;Deng B;Terman D. The bifurcation of homoclinic and periodic orbits from two heteroclinic orbits. {H}SIAM Journal on Mathematical Analysis, 1990
查看更多︾
相似文献 查看更多>>
54.210.61.41