Stochastically Permanent Analysis of a Non-Autonomous Holling Ⅱ Predator-Prey Model With a Complex Type of Noises

Asymptotic behaviour of a non‐autonomous multispecies Holling type II model with a complex type of noises

“…In this section, we simulate the solution of (4) to verify the theoretical findings in Sections 2–4. We employ the Milstein's method (Higham, 2001; Wei & Li, 2022) to approximate the system (4) over equal time interval $$$ \Delta =\left[{t}_k,{t}_{k+1}\right] $$$ by $$$$ {\displaystyle \begin{array}{c}{x}_i\left({t}_{k+1...$$…”

“…In this section, we simulate the solution of (4) to verify the theoretical findings in Sections 2-4. We employ the Milstein's method (Higham, 2001;Wei & Li, 2022) to approximate the system (4) over equal time interval Δ ¼ t k , t kþ1 ½ by…”

“…4) reduces to a non-autonomous Holling type II predator-prey model with a complex type of noises (Wei & Li, 2022) by setting r 1 t ð Þ > 0 and r 2 t ð Þ < 0;…”

“…However, most of these models concentrate on introducing stochasticity through linear environmental noise affecting the populations or the functional response, failing to account for the diverse impact of different noises on the dynamical system. To address this limitation, a pioneering approach was introduced, expanding the type of noises from simple linear perturbations to non-linear types in two autonomous models and a non-autonomous model, namely the stochastic SIR model with Beddington-DeAngelis functional response (Du & Nhu, 2017), the predator-prey model with Crowly-Martin type functional response (Guo et al, 2019) and the Holling type II predator-prey model (Wei & Li, 2022). In the current literature, there is a notable scarcity of discussions regarding stochastic non-autonomous multispecies Holling type II models with simple linear noise, let alone the exploration of stochastic versions with complex noise patterns.…”