Brauer-type eigenvalue inclusion sets of stochastic/irreducible tensors and positive definiteness of tensors

In this paper, Brauer-type eigenvalue inclusion sets of stochastic tensors and irreducible tensors are given, respectively. Some sufficient conditions of positive (semi-)definiteness of stochastic tensors are obtained. Furthermore, the stability of a high-order nonlinear system is analysed by positive definiteness of tensors.