A class of linear differential dynamical systems with fuzzy initial condition

Fuzzy Sets and Systems

Volumn 158, Issue 21, 2007, Pages 2339-2358

  Xu, Jiuping ^a   Liao, Zhigao ^a,b   Hu, Zhineng ^a  

^a SICHUAN UNIVERSITY   (China)

^b GUANGXI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Fuzzy differential equation; Fuzzy dynamical systems; Initial value of fuzzy number

Indexed keywords

DIFFERENTIAL EQUATIONS; FUZZY SETS; LINEAR SYSTEMS; MATRIX ALGEBRA; NUMBER THEORY; THEOREM PROVING;

FUZZY DYNAMICAL SYSTEMS; FUZZY NUMBER; LINEAR DIFFERENTIAL DYNAMICAL SYSTEMS;

DYNAMICAL SYSTEMS;

EID: 34548156679     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2007.04.016     Document Type: Article

References (46)

1. Abbasbandy S., and Allah Viranloo T. Numerical solution of fuzzy differential equation by Runge-Kutta method. Nonlinear Stud. 11 (2004) 117-129
2. Abbasbandy S., et al. Numerical methods for fuzzy differential inclusions. Comput. Math. Appl. 48 (2004) 1633-1641
3. Abbasbandy S., Nieto J.J., and Alavi M. Tuning of reachable set in one dimensional fuzzy differential inclusions. Chaos, Solitons & Fractals 26 (2005) 1337-1341
4. Babolian E., Sadeghi H., and Javadi Sh. Numerically solution of fuzzy differential equations by Adomian method. Appl. Math. Comput. 149 (2004) 547-557
5. Bede B., Rudas I.J., and Bencsik A.L. First order linear fuzzy differential equations under generalized differentiability. Inform. Sci. 177 (2007) 1648-1662
6. Buckley J.J., and Feuring T. Introduction to fuzzy partial differential equations. Fuzzy Sets and Systems 105 (1999) 241-248
7. Buckley J.J., and Feuring T. Fuzzy initial value problem for Nth order linear differential equations. Fuzzy Sets and Systems 121 (2001) 247-255
8. Y. Chalco-Cano, H. Roman-Flores, On new solutions of fuzzy differential equation, Chaos, Solitons & Fractals, in press.
9. Chen B., and Liu X. Reliable control design of fuzzy dynamical systems with time-varying delay. Fuzzy Sets and Systems 146 (2004) 349-374
10. Coddington E.A., and Levinson N. Theory of Ordinary Differential Equations (1955), McGraw-Hill, New York
11. Deimling K. Multivalued Differential Equations (1992), Walter de Gruyter, New York
12. Diamond P. Brief note on the variation of constants formula for fuzzy differential equations. Fuzzy Sets and Systems 129 (2002) 65-71
13. Diamond P., and Kloeden P.E. Metric Spaces of Fuzzy Set: Theory and Applications (1994), World Scientific, Singapore
14. Diamond P., and Watson P. Regularity of solution sets for differential inclusions quasiconcave in parameter. Appl. Math. Lett. 13 (2000) 31-35
15. Dubois D., and Prade H. Operations on fuzzy numbers. Internat. J. Systems Sci. 9 (1978) 613-626
16. Georgiou D.N., Nieto J.J., and Rodrguez-Lpez R. Initial value problems for higher-order fuzzy differential equations. Nonlinear Anal. 63 (2005) 587-600
17. Gnana Bhaskar T., et al. Revisiting fuzzy differential equations. Nonlinear Anal. 58 (2004) 351-358
18. Goetschel Jr. R., and Voxman W. Elementary fuzzy calculus. Fuzzy Sets and Systems 18 (1986) 31-43
19. Hirsch M.W., and Smale S. Differential Equation, Dynamical Systems and Linear Algebra (1974), Academic Press, New York
20. Hong L., and Sun J. Bifurcations of fuzzy nonlinear dynamical systems. Comm. Nonlinear Sci. Numer. Simulation 11 (2006) 1-12
21. Hüllermeier E. An approach to modeling and simulation of uncertain dynamical systems. Internat. J. Uncertainty Fuzziness Knowledge-Based Systems 5 (1997) 117-137
22. Hüllermeier E. Numerical methods for fuzzy initial value problems. Internat. J. Uncertainty Fuzziness Knowledge-Based Systems 7 (1999) 439-461
23. Kaleva O. Fuzzy differential equations. Fuzzy Sets and Systems 24 (1987) 301-317
24. Kaleva O. The Cauchy problem for fuzzy differential equations. Fuzzy Sets and Systems 35 (1990) 309-316
25. Kaleva O. A note on fuzzy differential equations. Nonlinear Anal. 64 (2006) 895-900
26. Kloeden P.E., et al. Quasi-flows and equations with nonlinear differentials. Nonlinear Anal. 51 (2002) 1143-1158
27. Lakshmikantham V., and Nieto J.J. Differential equations in metric spaces: an introduction and an application to fuzzy differential equations. Dynamics Contin. Discrete Impuls. Systems Ser. A Math. Anal. 10 (2003) 991-1000
28. Lakshmikantham V., and Tolstonogov A.A. Existence and interrelation between set and fuzzy differential equations. Nonlinear Anal. 55 (2003) 255-268
29. Nieto J.J. The Cauchy problem for continuous fuzzy differential equations. Fuzzy Sets and Systems 102 (1999) 259-262
30. Nieto J.J., and Rodriguez-Lopez R. Bounded solutions for fuzzy differential and integral equations. Chaos, Solitons & Fractals 27 (2006) 1376-1386
31. Nieto J.J., Rodriguez-Lopez R., and Franco D. Linear first-order fuzzy differential equations. Internat. J. Uncertainty Fuzziness Knowledge-Based Systems 14 (2006) 687-709
32. O'Regan D., Lakshmikantham V., and Nieto J.J. Initial and boundary value problems for fuzzy differential equations. Nonlinear Anal. 54 (2003) 405-415
33. Pearson D.W. A property of linear fuzzy differential equations. Appl. Math. Lett. 10 3 (1997) 99-103
34. Perko L. Differential Equations and Dynamical Systems (1991), Springer, New York
35. Prakash P., et al. Existence of solutions of fuzzy neutral differential equations in Banach spaces. Dynam. Systems Appl. 14 (2005) 407-417
36. Puri M.L., and Ralescu D.A. Fuzzy random variables. J. Math. Anal. Appl. 114 (1986) 409-422
37. Rashkovsky I., and Margaliot M. Nicholson's blowflies revisited: a fuzzy modeling approach. Fuzzy Sets and Systems 158 10 (2007) 1083-1096
38. Rojas-Medar M.A., et al. Fuzzy quasilinear spaces and applications. Fuzzy Sets and Systems 152 (2005) 173-190
39. Roman-Flores H., and Rojas-Medar M. Embedding of level-continuous fuzzy sets on Banach spaces. Inform. Sci. 144 (2002) 227-247
40. Seikkala S. On the fuzzy initial value problem. Fuzzy Sets and Systems 24 (1987) 319-330
41. Seikkala S., and Vorobiev D. Towards the theory of fuzzy differential equations. Fuzzy Sets and Systems 125 (2002) 231-237
42. Song S., and Wu C. Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations. Fuzzy Sets and Systems 110 (2000) 55-67
43. Song S., Wu C., and Xue X. Existence and uniqueness of Cauchy problem for fuzzy differential equations under dissipative conditions. Comput. Math. Appl. 51 (2006) 1483-1492
44. Stefanini L., Sorini L., and Guerra M.L. Parametric representation of fuzzy numbers and application to fuzzy calculus. Fuzzy Sets and Systems 157 (2006) 2423-2455
45. Wu C., and Song S. Existence theorem to the Cauchy problem of fuzzy differential equations under compactness-type conditions. Inform. Sci. 108 (1998) 123-134
46. Zadeh L.A. Fuzzy sets. Inform. Control 8 (1965) 338-353