In this article we compare the mean-square stability properties of the θ-Maruyama and θ-Milstein method that are used to solve stochastic differential equations. For the linear stability analysis, we propose an extension of the standard geometric Brownian motion as a test equation and consider...

We present the similarities and differences between one-dimensional (1D) and two-dimensional (2D) spatially localized, time periodic solutions in discrete nonlinear Hamiltonian systems. In particular, the types of modes their stability and their bifurcations are presented. We find that two...

In this paper, we present a new macro model which involves the effects that the probability of traffic interruption has on the car-following behavior through formulating the inner relationship between micro and macro variables. Linear stability analysis shows that consideration of the traffic...

In this paper the linear asymptotic mean-square stability of class of diagonally drift-implicit Runge–Kutta schemes (DDISRK) for the weak solution of systems of stochastic differential equations (SDEs) is investigated. We provide explicit structure of the stability matrices of this class of...