Bibliography for Autonomous Systems

unabridged

 

  1. On singularities of autonomous implicit ordinary differential equations
    Reissig, Gunther; Boche, Holger
    IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, v 50, n 7, July, 2003, p 922-931, Compendex.
  2. A Characteristic Equation for Non-autonomous Partial Functional Differential Equations
    Guhring, G.; Rabiger, F.; Schnaubelt, R.
    Journal of Differential Equations, 2002, vol. 181, no. 2, pp. 439-462, Ingenta.  
  3. Initial Value Problem to the Second Order Non-Autonomous Functional Differential-Iterative Equation
    Liu, X. P.; Jia, M.
    Acta Mathematica Sinica, 2002, vol. 45, no. 4, pp. 711-718, Ingenta.  
  4. Stability, instability, and bifurcation phenomena in non-autonomous differential equations.
    Langa, José A.; Robinson, James C.; Suárez, Antonio
    Nonlinearity 15 (2002), no. 3, 887--903, MathSciNet.  
  5. Application des fonctions symétriques à la résolution d'équations différentielles autonomes combinatoires. (French)
    [Applying symmetric functions to the solution of combinatorial autonomous differential equations]  
    Chiricota, Yves
    Discrete Math.  259  (2002),  no. 1-3, 71--90, MathSciNet.  
  6. A comparison of symplectic and Hamilton's principle algorithms for autonomous and non-autonomous systems of ordinary differential equations
    Cano, B.; Lewis, H.R.
    Applied Numerical Mathematics, v 39, n 3-4, December, 2001, p 289-306, Compendex.
  7. Periodic solution of linear autonomous neutral differential equations with delays
    Zhang, Dechang ; Rong, Haiwu
    Gongcheng Shuxue Xuebao/Chinese Journal of Engineering Mathematics, v 16, n 1, 1999, p 9-16 Language: Chinese, Compendex.
  8. Asymptotic Stability for Linear Autonomous Differential Equation with Several Delays
    Meng, F.; Ke, W.
    Annals of Differential Equations, 1998, vol. 14, no. 4, pp. 605-610, Ingenta.  
  9. Remarks on stability results for the solutions of certain fourth-order autonomous differential equations
    Wu, X.; Xiong, K.
    International Journal of Control, v 69, n 2, Jan 20, 1998, p 353-360, Compendex.
  10. Bifurcation of harmonic solutions for periodically perturbed autonomous differential equations from a manifold of equilibria
    Morassi, P.  
    Nonlinear Analysis, Theory, Methods & Applications, v 32, n 2, Apr, 1998, p 145-161, Compendex.
  11. Method of linear non-autonomous finite equation set solution on the basis of differential Taylor transforms
    Simonyan, S.O.; Avetisyan, A.G.
    Engineering Simulation, v 15, n 4, 1998, p 407-421, Compendex.
  12. On the set of harmonic solutions of periodically perturbed autonomous differential equations on manifolds
    Furi, Massimo; Spadini, Marco
    Nonlinear Analysis, Theory, Methods & Applications, v 29, n 8, Oct, 1997, p 963-970, Compendex.
  13. Long asymptotic correlation time for non-linear autonomous Ito's stochastic differential equation
    Mamontov, Yevgeny V.; Willander, Magnus
    Nonlinear Dynamics, v 12, n 4, Apr, 1997, p 399-411, Compendex.
  14. Experimental Chaos from Autonomous Electronic Circuits  
    Michael Peter Kennedy  
    Philosophical Transactions: Physical Sciences and Engineering, Vol. 353, No. 1701, Chaotic Behaviour in Electronic Circuits. (Oct. 16, 1995), pp. 13-32, Jstor.  
  15. Experimental Chaos from Non-Autonomous Electronic Circuits  
    M. Lakshmanan; K. Murali  
    Philosophical Transactions: Physical Sciences and Engineering, Vol. 353, No. 1701, Chaotic Behaviour in Electronic Circuits. (Oct. 16, 1995), pp. 33-46, Jstor.  
  16. Asymptotically Autonomous Semiflows: Chain Recurrence and Lyapunov Functions  
    Konstantin Mischaikow; Hal Smith; Horst R. Thieme  
    Transactions of the American Mathematical Society, Vol. 347, No. 5. (May, 1995), pp. 1669-1685, Jstor.  
  17. Uniform Asymptotic Stability for a Scalar Autonomous Differential Equation with "Maxima".
    Voulov, H. D.
    Mathematica Balkanica, 1995, vol. 9, no. 4, pp. 299, Ingenta.  
  18. Theory and Computation of Periodic Solutions of Autonomous Partial Differential Equation Boundary Value Problems, with Application to the Driven Cavity Problem.
    Gustafson, K.
    Mathematical and computer modelling, 1995, vol. 22, no. 9, pp. 57, Ingenta.  
  19. Constructing Lyapunov functions for certain fourth-order autonomous differential equations
    Tiryaki, A.; Tunc, C.
    Indian Journal of Pure and Applied Mathematics, v 26, n 3, 1995, p 225, Compendex.
  20. Lyapunov exponents analysis of autonomous and nonautonomous sets of ordinary differential equations
    Grygiel, K.; Szlachetka, P.
    Acta Physica Polonica, Series B: Particle Physics and Field Theory, Nuclear Physics Theory of Relativity, v 26, n 8, Aug, 1995, p 1321, Compendex.
  21. Method for finding the periodic solution of autonomous ordinary differential equations
    Jiang, Chang Jin
    Applied Mathematics and Computation (New York), v 66, n 2-3, Dec, 1994, p 161, Compendex.
  22. Necessary and sufficient conditions for oscillation of autonomous neutral differential equations with distributed delay
    Bainov, D.; Petrov, V.
    Journal of Mathematical Analysis and Applications, v 182, n 1, Feb 15, 1994, p 202, Compendex.
  23. Asymptotically autonomous differential equations in the plane. II. Stricter Poincaré/Bendixson type results.
    Thieme, Horst R.
    Differential Integral Equations 7 (1994), no. 5-6, 1625--1640, MathSciNet.  
  24. A non-autonomous differential equation to model bacterial growth.
    Baranyi, J.; Roberts, T.A.; McClure, P.
    Food microbiology, 1993, vol. 10, no. 1, pp. 43, Ingenta.  
  25. Oscillations in second order linear autonomous differential equations with distributed type deviating arguments
    Philos, Ch.G.; Purnaras, I.K.; Seicas, Y.G.
    Journal of Mathematical Analysis and Applications, v 176, n 2, Jul 1, 1993, p 458, Compendex.
  26. Two Timescale Harmonic Balance. I. Application to Autonomous One-Dimensional Nonlinear Oscillators  
    J. L. Summers; M. D. Savage  
    Philosophical Transactions: Physical Sciences and Engineering, Vol. 340, No. 1659. (Sep. 15, 1992), pp. 473-501, Jstor.  
  27. Continuation Theorems for Periodic Perturbations of Autonomous Systems
    Anna Capietto; Jean Mawhin; Fabio Zanolin
    Transactions of the American Mathematical Society, Vol. 329, No. 1. (Jan., 1992), pp. 41-72, Jstor.  
  28. A finite-difference method for solving the periodic problem for autonomous differential equations with maxima.
    Ba\u\i nov, D. D.; Kazakova, N. G.
    Math. J. Toyama Univ. 15 (1992), 1--13, MathSciNet.  
  29. Plane Autonomous Systems with Rational Vector Fields  
    Harold E. Benzinger  
    Transactions of the American Mathematical Society, Vol. 326, No. 2. (Aug., 1991), pp. 465-484, Jstor.  
  30. Homogeneous, isobaric, and autonomous algebraic differential equations
    Horwitz, Alan
    Journal of Mathematical Analysis and Applications, v 160, n 1, Sep 1, 1991, p 123, Compendex.
  31. Computational Aspects of Some Autonomous Differential Equations  
    J. M. Hammersley; G. Mazzarino  
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 424, No. 1866. (Jul. 8, 1989), pp. 19-37, Jstor.  
  32. On the structure of the solutions of an autonomous differential-delay system by the method of characteristic equation.
    Csato, S.
    Studia scientiarum mathematicarum Hungarica, 1989, vol. 24, no. 4, pp. 461, Ingenta.   
  33. Stability results for the solutions of certain fourth-order autonomous differential equations.
    Chin, Philip S. M.
    Internat. J. Control 49 (1989), no. 4, 1163--1173, MathSciNet.  
  34. Autonomous Bifurcations of a Simple Bimolecular Surface-Reaction Model  
    M. A. McKarnin; R. Aris; L. D. Schmidt  
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 415, No. 1849. (Feb. 9, 1988), pp. 363-387, Jstor.  
  35. The behavior of solutions in the vicinity of a bounded solution to autonomous differential equations.
    Lin, Guo Tian
    A Chinese summary appears in Chinese Ann. Math. Ser. A 7 (1986), no. 2, 239. Chinese Ann. Math. Ser. B 7 (1986), no. 2, 205--212, MathSciNet.  
  36. A Note on the Asymptotic Stability of Periodic Solutions of Autonomous Differential Equations (in Classroom Notes in Applied Mathematics)  
    H. Arthur de Kleine  
    SIAM Review, Vol. 26, No. 3. (Jul., 1984), pp. 417-421, Jstor.  
  37. Julia sets and autonomous differential equations.
    Barnsley, Michael F.; Harrington, Andrew N.
    Differential equations (Birmingham, Ala., 1983), 37--41, North-Holland Math. Stud., 92, North-Holland, Amsterdam, 1984, MathSciNet.  
  38. Chaotic Traveling Waves in General Autonomous Systems of Nonlinear Partial Differential Equations  
    Stephen C. Persek  
    SIAM Journal on Applied Mathematics, Vol. 42, No. 5. (Oct., 1982), pp. 1099-1110, Jstor.  
  39. Galerkin method for autonomous differential equations with unknown parameters.
    Yamamoto, Norio
    J. Math. Tokushima Univ. 16 (1982), 55--93, MathSciNet.  
  40. Galerkin method for autonomous differential equations.
    Shinohara, Yoshitane
    J. Math. Tokushima Univ. 15 (1981), 53--85, MathSciNet.  
  41. On Autonomous Control Systems on Certain Manifolds  
    Chao-Chu Liang  
    Proceedings of the American Mathematical Society, Vol. 79, No. 1. (May, 1980), pp. 63-66, Jstor.  
  42. Computational complexity of one-step methods for a scalar autonomous differential equation.
    Werschulz, A. G.
    Computing 23 (1979), no. 4, 345--355, MathSciNet.  
  43. Contributions to the study of the center for nonlinearizable autonomous differential equations. (Italian)
    Santoro, Paolo
    Riv. Mat. Univ. Parma (4) 5 (1979), part 2, 715--724 (1980), MathSciNet.  
  44. Asymptotically Autonomous Multivalued Differential Equations  
    James P. Foti  
    Transactions of the American Mathematical Society, Vol. 221, No. 2. (Aug., 1976), pp. 449-452, Jstor.  
  45. A Quadratically Convergent Iteration Method for Computing Zeros of Operators Satisfying Autonomous Differential Equations  
    L. B. Rall  
    Mathematics of Computation, Vol. 30, No. 133. (Jan., 1976), pp. 112-114, Jstor.  
  46. Periodic motion in a class of nth-order autonomous differential equations.
    Williamson, Darrell
    J. Math. Anal. Appl. 53 (1976), no. 3, 669--679, MathSciNet.  
  47. Asymptotic Behavior of Perturbed Autonomous Linear Functional Differential Equations  
    Richard B. Evans  
    Proceedings of the American Mathematical Society, Vol. 48, No. 2. (Apr., 1975), pp. 351-357, Jstor.  
  48. Asymptotic Stability for Some Critical Autonomous Differential Equations  
    Elliot Winston  
    Proceedings of the American Mathematical Society, Vol. 44, No. 2. (Jun., 1974), pp. 385-388, Jstor.  
  49. On Periodic Solutions of Autonomous Hamiltonian Systems of Ordinary Differential Equations  
    David C. Clark  
    Proceedings of the American Mathematical Society, Vol. 39, No. 3. (Aug., 1973), pp. 579-584, Jstor.  
  50. Erratum: Periodic Solutions of Perturbed Autonomous Systems, and Locking-In  
    Louis B. Bushard  
    SIAM Journal on Applied Mathematics, Vol. 25, No. 1. (Jul., 1973), p. 124, Jstor.  
  51. Periodic Solutions of Perturbed Autonomous Systems, and Locking-in  
    Louis B. Bushard  
    SIAM Journal on Applied Mathematics, Vol. 22, No. 4. (Jun., 1972), pp. 519-528, Jstor.  
  52. On the boundedness of solutions of some non-autonomous differential equations of the fourth-order.
    Sinha, A. S. C.; Hari, Y.
    Internat. J. Control (1) 15 (1972), 717--724, MathSciNet.  
  53. Quickly Oscillating Solutions of Autonomous Ordinary Differential Equations  
    Stephen R. Bernfeld; A. Lasota  
    Proceedings of the American Mathematical Society, Vol. 30, No. 3. (Nov., 1971), pp. 519-526, Jstor.  
  54. Stability and entering of the origin for real, nonlinear, autonomous differential equations of third order.
    Roberts, Charles E.; Belford, Geneva G.
    SIAM J. Math. Anal. 2 1971 133--148, MathSciNet.  
  55. A Global Existence Theorem for Autonomous Differential Equations in a Banach Space  
    R. H. Martin, Jr.  
    Proceedings of the American Mathematical Society, Vol. 26, No. 2. (Oct., 1970), pp. 307-314, Jstor.  
  56. The Invariance of Limit Sets for Autonomous Functional-Differential Equations  
    F. Kappel  
    SIAM Journal on Applied Mathematics, Vol. 19, No. 2. (Sep., 1970), pp. 408-419, Jstor.  
  57. Integral manifolds of a class of third order autonomous differential equations.
    Anderson, Larry R.
    J. Differential Equations 7 1970 274--286, MathSciNet.  
  58. A Method and New Results for Stability and Instability of Autonomous Functional Differential Equations  
    Daniel I. Barnea  
    SIAM Journal on Applied Mathematics, Vol. 17, No. 4. (Jul., 1969), pp. 681-697, Jstor.  
  59. On the Boundedness of Solutions of Classes of Multidimensional Nonlinear Autonomous Systems  
    Rui J. P. De Figueiredo; Chieng-Yi Chang  
    SIAM Journal on Applied Mathematics, Vol. 17, No. 4. (Jul., 1969), pp. 672-680, Jstor.  
  60. On the boundedness and the stability of solutions of some non-autonomous differential equations of the third order.
    Swick, K.
    J. London Math. Soc. 44 1969 347--359, MathSciNet.  
  61. Invariant Manifolds for Some Autonomous Systems  
    F. S. Van Vleck  
    Transactions of the American Mathematical Society, Vol. 107, No. 2. (May, 1963), pp. 186-196, Jstor.  
  62. An Existence Theorem for Certain Autonomous Systems  
    Z. A. Melzak  
    The American Mathematical Monthly, Vol. 67, No. 5. (May, 1960), pp. 438-442, Jstor.  
  63. Small Periodic Pertubations of an Autonomous System with a Stable Orbit  
    Norman Levinson  
    The Annals of Mathematics, 2nd Ser., Vol. 52, No. 3. (Nov., 1950), pp. 727-738, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004