Asymptotic equilibrium and stability of fuzzy differential equations. (English) Zbl 1084.34052

Song, Shiji; Wu, Cheng; Lee, E. S.

Comput. Math. Appl. 49, No. 7-8, 1267-1277 (2005).

The authors consider the asymptotic equilibrium of the following fuzzy differential equation \[ x'= f(t,x),\quad x(t_0)= x_0, \] with \(f\in C[J\times E^n, E^n]\), \(J= [t,\infty]\), \(x_0\in E^n\).
Moreover, they prove the asymptotic stability of the perturbed fuzzy differential equation \[ x'= A(t)x+ f(t,x),\quad x(t_0)= x_0, \] where \(f\in C[\mathbb{R}_+\times E^n, E^n]\), and for each \(t\in \mathbb{R}_+\), \(A(t): E^n\to E^n\) is a semilinear operator, by using Lyapunov’s direct method.
An example is discussed, too.

Reviewer: Jong Yeoul Park (Pusan)

MSC:

34D20	Stability of solutions to ordinary differential equations
34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34G25	Evolution inclusions

Keywords:

fuzzy differential equations; asymptotic equilibrium; Lyapunov stability

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