Stability in distribution of competitive Lotka–Volterra system with Markovian switching

Hu, Guixin; Ke, Wang

doi:10.1016/j.apm.2010.12.025

Cited by 27 publications

(5 citation statements)

References 7 publications

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“…In fact, there are several types of environmental noise. Besides the white noise there is also the telegraph noise (Hu and Wang, 2011;Mao, 2007, 2009;Li et al, 2009;Zhu and Yin, 2009). The latter can be demonstrated as a switching between two or more regimes of environment, which differ by factors such as the availability of food and climatic characteristics.…”

Section: Q3mentioning

confidence: 98%

On stochastic Gilpin–Ayala population model with Markovian switching

Settati¹,

Lahrouz²

2015

Biosystems

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Section: Q3mentioning

confidence: 98%

On stochastic Gilpin–Ayala population model with Markovian switching

Settati¹,

Lahrouz²

2015

Biosystems

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“…This model plays an important role in biomathematics applications, the dynamical behaviors of SDS (1.1) and its related stochastic models have been investigated recently in [10,14,15,17]. It is known that a unique strong solution exists for SDS (1.1), and that non-negativity of the initial value is preserved, see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…[10]) The solutions of SDS (1.1) in (x 0 , x0 , ) ∈ K + × K + × S, where x x 0 , t , x x0 , t are respectively two solutions of SDS (1.1) with initial values x 0 , x0 for any compact subset K + of R + , and ∈ S.…”

mentioning

confidence: 99%

Explicit numerical approximation for logistic models with regime switching in finite and infinite horizons

Li,

Yang

2021

Preprint

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The stochastic logistic model with regime switching is an important model in the ecosystem. While analytic solution to this model is positive, current numerical methods are unable to preserve such boundaries in the approximation. So, proposing appropriate numerical method for solving this model which preserves positivity and dynamical behaviors of the model's solution is very important. In this paper, we present a positivity preserving truncated Euler-Maruyama scheme for this model, which taking advantages of being explicit and easily implementable. Without additional restriction conditions, strong convergence of the numerical algorithm is studied, and 1/2 order convergence rate is obtained. In the particular case of this model without switching the first order strong convergence rate is obtained. Furthermore, the approximation of long-time dynamical properties is realized, including the stochastic permanence, extinctive and stability in distribution. Some simulations and examples are provided to confirm the theoretical results and demonstrate the validity of the approach.

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“…Noisy transition rates are often referred to as environmental stochasticity in epidemiology and ecology (Engen et al, 1998). The role of such stochasticity has been extensively studied, including in the context of deterministic ODE skeletons driven by diffusions (Dureau et al, 2013;Hu and Wang, 2011;Ionides et al, 2006;King et al, 2008) and driven by Lévy processes (Bhadra et al, 2011; Bretó et al (2009). This model will be used in Section 5 to illustrate our results.…”

Section: Introductionmentioning

confidence: 99%