A simple chaotic delay differential equation

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 366, Issue 4-5, 2007, Pages 397-402

  Sprott, J C ^a  

^a University of Wisconsin Madison   (United States)

Author keywords

Brownian motion; Chaos; Delay differential equation; Lyapunov exponent

Indexed keywords

BROWNIAN MOVEMENT; CHAOS THEORY; CHAOTIC SYSTEMS; CONTROL NONLINEARITIES; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS;

CHAOTIC DIFFUSION; DELAY DIFFERENTIAL EQUATIONS; HIGH-DIMENSIONAL; LYAPUNOV EXPONENT; LYAPUNOV EXPONENT SPECTRUM;

DIFFERENTIAL EQUATIONS;

EID: 34249037458     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2007.01.083     Document Type: Article

References (36)

1. Sprott J.C. Phys. Lett. A 228 (1997) 271
2. Gottlieb H.P.W., and Sprott J.C. Phys. Lett. A 291 (2001) 385
3. Thomas R., Basios V., Eiswirth M., Kruel T., and Rössler O.E. Chaos 14 (2005) 669
4. Malasani J.-M. Phys. Lett. A 264 (2000) 383
5. Linz S.J., and Sprott J.C. Phys. Lett. A 259 (1999) 240
6. Arneodo A., Coullet P., and Tresser C. Phys. Lett. A 79 (1980) 259
7. Vano J.A., Wildenberg J.C., Anderson M.B., Noel J.K., and Sprott J.C. Nonlinearity 19 (2006) 2391
8. Chlouverakis K.E., and Sprott J.C. Chaos Solitons Fractals 28 (2005) 739
9. Sprott J.C., Wildenberg J.C., and Azizi Y. Chaos Solitons Fractals 26 (2005) 1035
10. Bellen A., and Zennaro M. Numerical Methods for Delay Differential Equations (2003), Oxford Univ. Press
11. Kuang Y. Delay Differential Equations with Applications in Population Dynamics (1993), Academic Press, San Diego
12. Sharpe F.R., and Lotka A.J. Am. J. Hygiene 3 (1923) 96
13. Villasana M., and Radunskaya A. J. Math. Biol. 47 (2003) 270
14. Nelson P.W., and Perelson A.S. Math. Biosci. 179 (2002) 73
15. Brayton R.K. Quart. Appl. Math. 24 (1966) 215
16. Driver R.D. J. Differential Equations 54 (1984) 73
17. Mackey D., and Glass L. Science 197 (1977) 28
18. Farmer J.D. Physica D 4 (1982) 366
19. Grassberger P., and Procaccia I. Physica D 13 (1984) 34
20. Ikeda K., and Matsumoto K. Physica D 29 (1987) 223
21. Ikeda K. Opt. Commun. 39 (1979) 257
22. Dubinov A.E., and Dubinova I.D. J. Plasma Phys. 71 (2005) 715
23. Murray J.D. Mathematical Biology. second ed. (1993), Springer, New York
24. Feigenbaum M.J. J. Stat. Phys. 19 (1978) 24
25. Wolf A., Swift J.B., Swinney H.L., and Vastano J.A. Physica D 16 (1985) 285
26. Kaplan J., and Yorke J. In: Peitgen H.-O., and Walther H.-O. (Eds). Functional Differential Equations and Approximations of Fixed Points. Lecture Notes in Mathematics vol. 730 (1979), Springer, Berlin 228-237
27. Pesin Ya.B. Russian Math. Surv. 32 (1977) 55
28. Press W.H., Flannery B.P., Teukolsky S.A., and Vetterling W.T. Numerical Recipes: The Art of Scientific Computing. second ed. (1992), Cambridge Univ. Press
29. Hurst H.E., Black R.P., and Simaika Y.M. Long-Term Storage: An Experimental Study (1965), Constable, London
30. Hutchinson G.E. Ann. N.Y. Acad. Sci. 50 (1948) 221
31. May R.M. Stability and Complexity in Model Ecosystems. second ed. (1975), Princeton Univ. Press
32. Suarez M.J., and Schopf P.S. J. Atmos. Sci. 45 (1988) 3283
33. Mykolaitis G., Tamaševičius A., Cenys A., Bumeliene S., Anagnostopoulos A.N., and Kalkan N. Chaos Solitons Fractals 17 (2003) 343
34. Namajunas A., Pyragas K., and Tamaševičius A. Int. J. Bifur. Chaos 7 (1997) 957
35. Namajunas A., Pyragas K., and Tamaševičius A. Phys. Lett. A 201 (1995) 42
36. Pyragas K., and Tamševičius A. Phys. Lett. A 180 (1993) 99