Stability and periodicity in fuzzy differential equations

Abstract

Formulations of fuzzy differential equations (DEs) in terms of the Hukuhara derivative do not reproduce the rich and varied behavior of crisp DEs. A recent interpretation in terms of differential inclusions, expressed level setwise, overcomes much of this deficiency and opens up for profitable investigation such properties as stability, attraction, periodicity, and the like. This is especially important for investigating continuous systems, which are uncertain or incompletely specified. This paper studies Lyapunov stability of fuzzy DEs and the periodicity of the fuzzy solution set for both the time-dependent and autonomous cases