Endotactic Networks and Toric Differential Inclusions

THE FULL AVERAGING OF FUZZY DIFFERENTIAL INCLUSIONS

In this paper the substantiation of the method of full averaging for fuzzy differential inclusions is considered. These results generalize the results of [17, 20] for differential inclusions with Hukuhara derivative and of [18] for fuzzy differential equations.

Improving the Solution of Fuzzy Differential Inclusions

Covering dimension and differential inclusions

In this paper we shall establish a result concerning the covering dimension of a set of the type {x ∈ X : Φ(x)∩Ψ(x) 6= ∅}, where Φ, Ψ are two multifunctions from X into Y and X, Y are real Banach spaces. Moreover, some applications to the differential inclusions will be given.

Stochastic Approximations and Differential Inclusions

The dynamical systems approach to stochastic approximation is generalized to the case where the mean differential equation is replaced by a differential inclusion. The limit set theorem of Benäım and Hirsch is extended to this situation. Internally chain transitive sets and attractors are studied in detail for set-valued dynamical systems. Applications to game theory are given, in particular to...

Themes on Differential Inclusions (

An ordinary differential equation x = f (t, x(t)) (ODE) uniquely assigns the time derivative x (t) = d dt x(t) as a function of t and x. A differential inclusion x ∈ F (t, x(t)), (DI) on the other hand, only requires that the derivative x be inside a given set F (t, x) ⊂ R n. Therefore, given an initial condition x(0) = ¯ x, one can usually find several solutions of (DI). f(x) x _ x _ x x F(x) ...