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Abstract: This paper is concerned with a predator–prey system with Holling II functional response and hunting delay and gestation. By regarding the sum of delays as the bifurcation parameter, the local stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. We obtained explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation. Using a global Hopf bifurcation result of Wu [Wu JH. Symmetric functional differential equations and neural networks with memory, Trans Amer Math Soc 1998;350:4799–4838] for functional differential equations, we may show the global existence of the periodic solutions. Finally, several numerical simulations illustrating the theoretical analysis are also given. [Copyright &y& Elsevier]

Abstract: The main goal of the present paper is to find computable stability criteria for two-dimensional stochastic systems based on Kronecker product and nonnegative matrices theory. First, 2-D discrete stochastic system model is established by extending system matrices of the well-known Fornasini–Marchesiniʼs second model into stochastic matrices. The elements of these stochastic matrices are second-order, weakly stationary white-noise sequences. Second, a necessary and sufficient condition for 2-D stochastic systems is presented, this is the first time that has been proposed. Third, computable mean-square asymptotic stability criteria are derived via Kronecker product and the nonnegative matrix theory. The criteria are only sufficient conditions. Finally, illustrative examples are provided. [Copyright &y& Elsevier]