scholarly journals Survival and stationary distribution of a stochastic facultative mutualism model with distributed delays and strong kernels

2021 ◽  
Vol 18 (4) ◽  
pp. 3160-3179
Author(s):  
Ke Qi ◽  
◽  
Zhijun Liu ◽  
Lianwen Wang ◽  
Qinglong Wang
Keyword(s):  
Stationary Distribution ◽  
Distributed Delays ◽  
Facultative Mutualism ◽  
Mutualism Model

The stationary distribution and ergodicity of a stochastic mutualism model

2018 ◽  
Vol 68 (3) ◽  
pp. 685-690 ◽  
Author(s):  
Jingliang Lv ◽  
Sirun Liu ◽  
Heng Liu
Keyword(s):  
Stochastic Model ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Ergodic Property ◽  
Model Simulations ◽  
Analytical Results ◽  
Stationary Distribution And Ergodicity ◽  
Mutualism Model ◽  
Mutualism System

Abstract This paper is concerned with a stochastic mutualism system with toxicant substances and saturation terms. We obtain the sufficient conditions for the existence of a unique stationary distribution to the equation and it has an ergodic property. It is interesting and surprising that toxicant substances have no effect on the stationary distribution of the stochastic model. Simulations are also carried out to confirm our analytical results.

Survival analysis of an impulsive stochastic facultative mutualism system with saturation effect

2020 ◽  
pp. 2150009
Author(s):  
Siyu Chen ◽  
Zhijun Liu ◽  
Ronghua Tan ◽  
Lianwen Wang
Keyword(s):  
Noise Source ◽  
Saturation Effect ◽  
Stochastic Permanence ◽  
Facultative Mutualism ◽  
Coupling Noise ◽  
Time Average ◽  
Mutualism Model ◽  
Model Subject ◽  
White Noises ◽  
Mutualism System

A system of impulsive stochastic differential equations is proposed as a two-species facultative mutualism model subject to impulsive and two coupling noise source perturbations, in which the saturation effect is taken into account. A set of sufficient criteria for extinction (exponential extinction and extinction) and permanence (permanence in time average and stochastic permanence) of the system are established. Extensive simulation figures are demonstrated to support the theoretical findings. Meanwhile, we look at the effects of coupling white noises, impulses, intrinsic growth rates, intra-specific competition rates and inter-specific mutualism rates on the survival of populations.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

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