Stochastic Nicholson’s blowflies delayed differential equations

Stochastic Nicholson’s blowflies delay differential equation with regime switching

“…• We show the global existence of almost surely positive solution to equation (1.2) without the restricted condition δ i > σ 2 i /2, i ∈ S, which extends the one in [3]; • We give the estimations of lim sup t→∞ E[X θ (t)], lim sup t→∞ 1 t t 0 E[X θ (s)]ds, lim inf t→∞ X(t) and the sample Lyapunov exponent of X(t), which are more general than the ones in literature.…”

“…Considering that the per capita daily adult death rate δ is affected by the white noise of the environment, one often uses δ − σdB(t) in lieu of δ, where σ denotes the intensity of the white noise and B(t) is a one-dimensional Brownian motion defined on (Ω, {F t } t 0 , P), which is a complete probability space. Wang et al (2019) [3] studied the following stochastic Nicholson's blowflies delay differential equation: t 0 E[X(s)]ds, respectively. But we find from numerical simulation that the condition δ > σ 2 /2 is too strict to the nonexplosion of the solution to equation (1.1).…”

Stochastic delay differential neoclassical growth model

“…Moreover, we deduce the simple sufficient condition α > σ 2 2 that guarantees the global positive solution of (1.3) exists uniquely, and we estimate its ultimate boundedness and sample Lyapunov exponent. In particular, all results of [22] are the special situations of this paper with γ = 1. It is easy to see that if environmental noises are sufficiently large such that the condition α > σ 2 2 does not hold, then Lemma 2.2, Theorems 3.1 and 3.2 are invalid.…”

Lyapunov stability analysis for nonlinear delay systems under random effects and stochastic perturbations with applications in finance and ecology

“…Stochastic models are proposed to capture the uncertainty and variations in the transmission of the diseases. Many recent works dedicated to stochastic epidemiological and ecological models can be found in [37,38,40,41,50,52,[58][59][60][61]. There is still considerable uncertainty with regard to the study of stability, therefore we have addressed the stochastic global exponential and practical stability.…”

“…The species become extinct due to the global stability of the zero solution of (5), see [31]. Many authors have studied the dynamics of this equation [31][32][33][34][35], and stochastically [36][37][38].…”