On the stability of fuzzy dynamical systems

Fuzzy dynamical systems and Invariant attractor sets for fuzzy strongly continuous semigroups

“…we can verify that its solution is given by T (t)x 0 = e −kt x 0 and that the origin is an asymptotically stable equilibrium point for k > 0. By Proposition 3.1, we have that χ {0} is an equilibrium point of T (t), sincex = 0 is an equilibrium point of (2). Moreover, from corollary 3.1 χ {0} is asymptotically stable.…”

“…and the nature of the stability of such equilibrium points. New results about equilibrium points are presented in [2]. In [1], M.S.…”

Estimativa da Condição Inicial Fuzzy para Modelos de Biomatemática via Métodos Estatı́sticos

“…Proposta por Lotfi A. Zadeh em 1965 [13], a teoria dos conjuntos fuzzy busca representar matematicamente grandezas incertas. Esta ideia já foi extensivamente adotada para representar a condição inicial em sistemas dinâmicos, por exemplo em [3,11], ou especificamente para tratar da condição inicial de modelos voltados a fenômenos biológicos [1].…”

Complex fuzzy dynamical systems and Stability of the equilibrium Point

“…Mizukoshi et al showed in [9] that the family of applications φ t , indexed by t ∈ R, obtained by Zadeh's extension(see [13]) on initial condition of φ t , satisfies conditions that characterize φ t as a dynamical system in the metric space E n . The stability of fuzzy dynamical systems is presented in [2,8]. Since D. Ramot introduced a new concept in the context of fuzzy sets theory (complex fuzzy set) and there are many examples of application namely solar activity, signal processing, etc (see [12]).…”