메뉴 건너뛰기




Volumn 351, Issue 3, 1999, Pages 901-945

Erratic solutions of simple delay equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 22444452217     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-99-02351-x     Document Type: Article
Times cited : (31)

References (37)
  • 1
    • 0001009039 scopus 로고
    • Existence of chaos in control systems with delayed feedback
    • [AdHW] MR 85a:58061
    • [AdHW] U. An der Heiden and H.-O. Walther, Existence of chaos in control systems with delayed feedback, J. Diff. Equs. 47 (1983), 273-295. MR 85a:58061
    • (1983) J. Diff. Equs. , vol.47 , pp. 273-295
    • An Der Heiden, U.1    Walther, H.-O.2
  • 4
    • 21844481996 scopus 로고
    • Floquet multipliers and secondary bifurcations in functional differential equations Numerical and analytical results
    • [DL-W] MR 97f:34047
    • [DL-W] P. Dormayer and B. Lani-Wayda, Floquet multipliers and secondary bifurcations in functional differential equations: Numerical and analytical results, Z. Angew. Math. Phys. (ZAMP) 46 (1995), 823-858. MR 97f:34047
    • (1995) Z. Angew. Math. Phys. (ZAMP) , vol.46 , pp. 823-858
    • Dormayer, P.1    Lani-Wayda, B.2
  • 5
    • 0004034650 scopus 로고
    • [Dr] Applied Mathematical Sciences 20 Springer Verlag, New York, MR 57:16897
    • [Dr] R.D. Driver, Ordinary and delay differential equations, (Applied Mathematical Sciences 20) Springer Verlag, New York, 1977. MR 57:16897
    • (1977) Ordinary and Delay Differential Equations
    • Driver, R.D.1
  • 8
    • 40749093037 scopus 로고
    • Measuring the strangeness of strange attractors
    • [GP] MR 85i:58071
    • [GP] P. Grassberger and I. Procaccia, Measuring the strangeness of strange attractors, Physica 9D (1983), 189-208. MR 85i:58071
    • (1983) Physica , vol.9 , pp. 189-208
    • Grassberger, P.1    Procaccia, I.2
  • 10
    • 0010935162 scopus 로고
    • Symbolic dynamics and nonlinear semiflows
    • [HL1] MR 89g:58130
    • [HL1] J.K. Hale and X.B. Lin, Symbolic dynamics and nonlinear semiflows, Ann. Mat. Pura Appl. (4) 144 (1986), 229-259. MR 89g:58130
    • (1986) Ann. Mat. Pura Appl. (4) , vol.144 , pp. 229-259
    • Hale, J.K.1    Lin, X.B.2
  • 11
    • 0007013021 scopus 로고
    • Examples of transverse homoclinic orbits in delay equations
    • [HL2] MR 87i:34087
    • [HL2] J.K. Hale and X.B. Lin, Examples of transverse homoclinic orbits in delay equations, Nonlinear Analysis 10 (1986), 693-709. MR 87i:34087
    • (1986) Nonlinear Analysis , vol.10 , pp. 693-709
    • Hale, J.K.1    Lin, X.B.2
  • 12
    • 0000702457 scopus 로고
    • Onset of Chaos in Differential Delay Equations
    • [HS] MR 89h:58115
    • [HS] J.K. Hale and N. Sternberg, Onset of Chaos in Differential Delay Equations, J. Computational Phys. 77 No.1 (1988), 221-239. MR 89h:58115
    • (1988) J. Computational Phys. , vol.77 , Issue.1 , pp. 221-239
    • Hale, J.K.1    Sternberg, N.2
  • 13
    • 0003324723 scopus 로고
    • Introduction to Functional Differential Equations
    • [HV-L] Springer Verlag, New York, MR 94m:34169
    • [HV-L] J.K. Hale and S.M. Verduyn-Lunel, Introduction to Functional Differential Equations, (Applied Mathematical Sciences 99), Springer Verlag, New York, 1993. MR 94m:34169
    • (1993) Applied Mathematical Sciences , vol.99
    • Hale, J.K.1    Verduyn-Lunel, S.M.2
  • 14
    • 0010939478 scopus 로고
    • Unstable hyperbolic periodic solutions of differential delay equations
    • [ILW] ed. R.P. Agarwal, World Scientific, Singapore, MR 93h:34125
    • [ILW] A. Ivanov, B. Lani-Wayda and H.-O. Walther, Unstable hyperbolic periodic solutions of differential delay equations, Recent Trends in Differential Equations, ed. R.P. Agarwal, World Scientific, Singapore, 1992, pp. 301-316. MR 93h:34125
    • (1992) Recent Trends in Differential Equations , pp. 301-316
    • Ivanov, A.1    Lani-Wayda, B.2    Walther, H.-O.3
  • 15
    • 0025483092 scopus 로고
    • Chaotic behavior in simple dynamical systems
    • [KS] MR 91e:58141
    • [KS] U. Kirchgraber and D. Stoffer, Chaotic behavior in simple dynamical systems, SIAM Review 32 No. 3 (1990), 424-452. MR 91e:58141
    • (1990) SIAM Review , vol.32 , Issue.3 , pp. 424-452
    • Kirchgraber, U.1    Stoffer, D.2
  • 16
    • 0000874319 scopus 로고
    • On the stability of a periodic solution of a differential delay equation
    • [KY] MR 501:13812
    • [KY] J.L. Kaplan and J.A. Yorke, On the stability of a periodic solution of a differential delay equation, SIAM J. Math. Analysis 6 (1975), 268-282. MR 501:13812
    • (1975) SIAM J. Math. Analysis , vol.6 , pp. 268-282
    • Kaplan, J.L.1    Yorke, J.A.2
  • 17
    • 0007015537 scopus 로고
    • Persistence of Poincaré mappings in functional differential equations (with application to structural stability of complicated behavior)
    • [L-W1] MR 96e:34118
    • [L-W1] B. Lani-Wayda, Persistence of Poincaré mappings in functional differential equations (with application to structural stability of complicated behavior), J. Dyn. Diff. Equs. 7 No. 1 (1995), 1-71. MR 96e:34118
    • (1995) J. Dyn. Diff. Equs. , vol.7 , Issue.1 , pp. 1-71
    • Lani-Wayda, B.1
  • 18
    • 0040618778 scopus 로고
    • Hyperbolic Sets, Shadowing and Persistence for Noninvertible Mappings in Banach spaces
    • [L-W2] Longman Group Ltd., Harlow, Essex, CMP 98:01
    • [L-W2] B. Lani-Wayda, Hyperbolic Sets, Shadowing and Persistence for Noninvertible Mappings in Banach spaces, Research Notes in Mathematics No. 334, Longman Group Ltd., Harlow, Essex, 1995. CMP 98:01
    • (1995) Research Notes in Mathematics No. , vol.334
    • Lani-Wayda, B.1
  • 19
    • 84972492596 scopus 로고
    • Chaotic motion generated by delayed negative feedback, Part i A transversality criterion
    • [L-WW1] MR 96c:58115
    • [L-WW1] B. Lani-Wayda and H.-O. Walther, Chaotic motion generated by delayed negative feedback, Part I: A transversality criterion, Diff. Int. Equs. 8 No. 6 (1995), 1407-52. MR 96c:58115
    • (1995) Diff. Int. Equs. , vol.8 , Issue.6 , pp. 1407-1452
    • Lani-Wayda, B.1    Walther, H.-O.2
  • 20
    • 0001282321 scopus 로고    scopus 로고
    • Chaotic motion generated by delayed negative feedback, Part II Construction of nonlinearities
    • [L-WW2] MR 97g:58147
    • [L-WW2] B. Lani-Wayda, and H.-O. Walther, Chaotic motion generated by delayed negative feedback, Part II: Construction of nonlinearities, Math. Nachr. 180 (1996), 141-211. MR 97g:58147
    • (1996) Math. Nachr. , vol.180 , pp. 141-211
    • Lani-Wayda, B.1    Walther, H.-O.2
  • 21
    • 0007012083 scopus 로고
    • Ergodic problems in biology
    • [La] MR 58:9378
    • [La] A. Lasota, Ergodic problems in biology, Asterisque 50 (1977), 239-250. MR 58:9378
    • (1977) Asterisque , vol.50 , pp. 239-250
    • Lasota, A.1
  • 22
    • 33646920470 scopus 로고
    • [Laz] Preprint 94-47, Université de Paris-Sud, Mathématiques, Bâtiment 425, 91405 Orsay, France
    • [Laz] V.A. Lazutkin, Positive Entropy for the Standard Map I, Preprint 94-47, Université de Paris-Sud, Mathématiques, Bâtiment 425, 91405 Orsay, France, 1994.
    • (1994) Positive Entropy for the Standard Map i
    • Lazutkin, V.A.1
  • 23
    • 0001995554 scopus 로고
    • Matematyczne problemy dynamiki ukladu krwinek czerwonych
    • [LWCz]
    • [LWCz] A. Lasota and M. Wazewska-Czyzewska, Matematyczne problemy dynamiki ukladu krwinek czerwonych, Mat. Stosowana 6 (1976), 23-40.
    • (1976) Mat. Stosowana , vol.6 , pp. 23-40
    • Lasota, A.1    Wazewska-Czyzewska, M.2
  • 24
    • 0000100336 scopus 로고
    • Period three implies chaos
    • [LY] MR 52:5898
    • [LY] T.Y. Li and J.A. Yorke, Period three implies chaos, Am. Math. Monthly 82 (1977), 985-992. MR 52:5898
    • (1977) Am. Math. Monthly , vol.82 , pp. 985-992
    • Li, T.Y.1    Yorke, J.A.2
  • 25
    • 0017714604 scopus 로고
    • Oscillation and chaos in physiological control systems
    • [MG]
    • [MG] M.C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science 197 (1977), 287-295.
    • (1977) Science , vol.197 , pp. 287-295
    • Mackey, M.C.1    Glass, L.2
  • 26
    • 0002815390 scopus 로고
    • A one-to-one representation of geodesics on a surface of negative curvature
    • [M]
    • [M] M. Morse, A one-to-one representation of geodesics on a surface of negative curvature, Am. J. Math. 43 (1921), 33-51.
    • (1921) Am. J. Math. , vol.43 , pp. 33-51
    • Morse, M.1
  • 27
    • 0000015923 scopus 로고
    • Symbolic Dynamics
    • [MH]
    • [MH] M. Morse and G. Hedlund, Symbolic Dynamics , Am. J. Math. 60 (1938), 815-866.
    • (1938) Am. J. Math. , vol.60 , pp. 815-866
    • Morse, M.1    Hedlund, G.2
  • 28
    • 0000226142 scopus 로고
    • Morse decompositions for delay differential equations
    • [M-P] MR 89m:58182
    • [M-P] J. Mallet-Paret, Morse decompositions for delay differential equations, J. Diff. Equs. 72 (1988), 270-315. MR 89m:58182
    • (1988) J. Diff. Equs. , vol.72 , pp. 270-315
    • Mallet-Paret, J.1
  • 29
    • 0030102885 scopus 로고    scopus 로고
    • The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay
    • [M-PS] MR 97a:34193b
    • [M-PS] J. Mallet-Paret and G. Sell, The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay, J. Diff. Eqns. 125 (1996), 441-489. MR 97a:34193b
    • (1996) J. Diff. Eqns. , vol.125 , pp. 441-489
    • Mallet-Paret, J.1    Sell, G.2
  • 30
    • 0001051330 scopus 로고
    • The Poincaré-Bendixson theorem for monotone cyclic feedback systems
    • [M-PSm] MR 91k:58098
    • [M-PSm] J. Mallet-Paret and H.L. Smith, The Poincaré-Bendixson theorem for monotone cyclic feedback systems, J. Dyn. Diff. Equs. 2 (1990), 367-421. MR 91k:58098
    • (1990) J. Dyn. Diff. Equs. , vol.2 , pp. 367-421
    • Mallet-Paret, J.1    Smith, H.L.2
  • 32
    • 0001261668 scopus 로고
    • Exponential dichotomies, the shadowing lemma and transversal homoclinic points
    • [P] U. Kirchgraber and H.-O. Walther (eds.), Teubner-Wiley, Stuttgart/Chichester, MR 89j:58060
    • [P] K.J. Palmer, Exponential dichotomies, the shadowing lemma and transversal homoclinic points, U. Kirchgraber and H.-O. Walther (eds.), Dynamics Reported, vol. I, Teubner-Wiley, Stuttgart/Chichester, 1988, pp. 265-306. MR 89j:58060
    • (1988) Dynamics Reported , vol.1 , pp. 265-306
    • Palmer, K.J.1
  • 33
    • 84968514104 scopus 로고
    • Differentiate Dynamical Systems
    • [S] MR 37:3598
    • [S] S. Smale, Differentiate Dynamical Systems, Bull. AMS 73 (1967), 747-817. MR 37:3598
    • (1967) Bull. AMS , vol.73 , pp. 747-817
    • Smale, S.1
  • 35
    • 0007013777 scopus 로고
    • Homoclinic solution and chaos in ẋ(t) = f(x(t - 1))
    • [W1] MR 83a:58060
    • [W1] H.-O. Walther, Homoclinic solution and chaos in ẋ(t) = f(x(t - 1)), Nonlinear Analysis 5 (1981), 775-788. MR 83a:58060
    • (1981) Nonlinear Analysis , vol.5 , pp. 775-788
    • Walther, H.-O.1
  • 36
    • 0003290464 scopus 로고
    • Hyperbolic periodic solutions, heteroclinic connections and transversal homoclinic points in autonomous differential delay equations
    • [W2] MR
    • [W2] H.-O. Walther, Hyperbolic periodic solutions, heteroclinic connections and transversal homoclinic points in autonomous differential delay equations, Memoirs AMS 402 (1989). MR 90m:58184
    • (1989) Memoirs AMS , vol.402 , pp. 58184
    • Walther, H.-O.1
  • 37
    • 0003195186 scopus 로고
    • The 2-dimensional attractor of x′(t) = -μx(t)+f(x(t - 1))
    • [W3] MR 95f:58070
    • [W3] H.-O. Walther, The 2-dimensional attractor of x′(t) = -μx(t)+f(x(t - 1)). Memoirs AMS 544 (1995). MR 95f:58070
    • (1995) Memoirs AMS , vol.544
    • Walther, H.-O.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.