A Finite Set Intersection Theorem
Suppose 0, ⩽ r m , and ℱ is a family of k -subsets of an n -set such that the intersection of any two different members of ℱ has cardinality congruent to r (mod m ). If k ≢ r (mod m ) then ❘ℱ❘ ⩽ n . The case of equality is also investigated.
In this paper, we study the nonnegative periodic dynamics of the delayed Cohen-Grossberg neural networks with discontinuous activation functions and periodic interconnection coefficients, self-inhibitions, and external inputs. Filippov theory is utilized to study the viability, namely, the existence of the solution of the Cauchy problem. Under some conditions, the existence and the asymptotical stability of a periodic solution are derived. Numerical examples are provided to illustrate the theoretical results.