We mainly prove: Assume that each output function of DCNN is bounded on R and satisfies the Lipschitz condition, if is a periodic function with period ω each i, then DCNN has a unique ω-period solution and all other solutions of DCNN converge exponentially to it, where is a Lipschitz constant of for i=1,2,...,n.
In this paper we study some properties of the distribution function of the random variable C(X,Y) when the copula of the random pair (X,Y) is M (respectively, W) - the copula for which each of X and Y is almost surely an increasing (respectively, decreasing) function of the other -, and C is any copula. We also study the distribution functions of M(X,Y) and W(X,Y) given that the joint distribution function of the random variables X and Y is any copula.
We characterize some bivariate semicopulas and, among them, the semicopulas satisfying a Lipschitz condition. In particular, the characterization of harmonic semicopulas allows us to introduce a new concept of depedence between two random variables. The notion of multivariate semicopula is given and two applications in the theory of fuzzy measures and stochastic processes are given.