A univariate first order stochastic cycle can be represented as an element of a bivariate first order vector autoregressive process, or VAR(1), where the transition matrix is associated with a Givens rotation. From the geometrical viewpoint, the kernel of the cyclical dynamics is described by a...

In this paper, a stochastic Holling II one-predator two-prey system with jumps is investigated. Firstly, the properties of the solution, such as the existence and uniqueness of the global positive solution, stochastic ultimate boundedness and the pathwise estimation are studied. Then we mainly...

We study a variation of the SIR (Susceptible/Infected/Recovered) dynamics on the complete graph, in which infected individuals may only spread to neighboring susceptible individuals at fixed rate λ0 while recovered individuals may only spread to neighboring infected individuals at fixed rate 1....

We develop a computationally efficient methodology to evaluate optimal management in a spatially and temporally dynamic bioeconomic system. The method involves standard techniques from the macroeconomics literature to calculate approximately optimal linear decision rules. Iterations between the...