A class of generalized Ginzburg–Landau equations with random switching

A class of numerical algorithms for stochastic differential equations with randomly varying truncations

“…where k ≥ 1 is an integer, and a(•), c(•), h(•) are bounded integrable functions on [0, ∞) and c(t) ≥ 0 for any t ≥ 0. Using the ideas in Kloeden and Platen [11, p. 125] and Wu et al [25], we get an explicit representation of the solution as…”

“…Then by virtue of Wu et al [25,Theorem 2.1], for any initial condition x 0 > 0, there is a unique positive solution of (2.6) on t ≥ 0. In fact, the solution can be explicitly given.…”

Two-Time-Scale Regime-Switching Stochastic Kolgomorov Systems With Wideband Noises

“…Recently, much effort has been devoted to stochastic Kolmogorov systems because their wide range of applications in statistical physics, ecology, and mathematical biology, among others. For example, there have been resurgent and emerging interests in studying Ginzburg-Landau equations [10] (see also [37]) in statistical physics, Lotka-Volterra models in statistical mechanics of population [21] (see also [9] for such equations with functional responses), the study of ecological models [7,24], and the work on infectious disease modeling [25] among others. For multi-dimensional Kolmogorov systems, the paper [14] nearly completely classified the "threshold" of coexistence and extinction.…”