Asymptotic behavior of a Lotka–Volterra food chain stochastic model in the Chemostat

2017 ◽  
Vol 35 (4) ◽  
pp. 645-661 ◽  
Author(s):  
Mingjuan Sun ◽  
Qinglai Dong ◽  
Jing Wu
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Model ◽  
Food Chain

scholarly journals Asymptotic Behavior Analysis for a Three-Species Food Chain Stochastic Model with Regime Switching

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Junmei Liu ◽  
Yonggang Ma
Keyword(s):  
Asymptotic Behavior ◽  
Lyapunov Function ◽  
Stochastic Model ◽  
Numerical Simulations ◽  
Behavior Analysis ◽  
Food Chain ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Stationary Distributions ◽  
Theoretical Results

This paper discusses the asymptotic behavior of a class of three-species stochastic model with regime switching. Using the Lyapunov function, we first obtain sufficient conditions for extinction and average time persistence. Then, we prove sufficient conditions for the existence of stationary distributions of populations, and they are ergodic. Numerical simulations are carried out to support our theoretical results.

Asymptotic behavior and stability of a stochastic model for AIDS transmission

2008 ◽  
Vol 204 (1) ◽  
pp. 99-108 ◽  
Author(s):  
Yongsheng Ding ◽  
Min Xu ◽  
Liangjian Hu
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Model

scholarly journals Interacting branching processes and linear file-sharing networks

2010 ◽  
Vol 42 (03) ◽  
pp. 834-854 ◽  
Author(s):  
Lasse Leskelä ◽  
Philippe Robert ◽  
Florian Simatos
Keyword(s):  
Communication Network ◽  
Asymptotic Behavior ◽  
Distributed Systems ◽  
Stochastic Model ◽  
Branching Processes ◽  
File Sharing ◽  
Independent Interest ◽  
Constant Flow

File-sharing networks are distributed systems used to disseminate files among nodes of a communication network. The general simple principle of these systems is that once a node has retrieved a file, it may become a server for this file. In this paper, the capacity of these networks is analyzed with a stochastic model when there is a constant flow of incoming requests for a given file. It is shown that the problem can be solved by analyzing the asymptotic behavior of a class of interacting branching processes. Several results of independent interest concerning these branching processes are derived and then used to study the file-sharing systems.

A Stochastic Model with Saturation Infection for Internal HIV Dynamics

2015 ◽  
Vol 713-715 ◽  
pp. 1546-1551 ◽  
Author(s):  
Jin Qiang Wang ◽  
Mao Xing Liu
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Model ◽  
Numerical Simulations ◽  
Infection Rate ◽  
Virus Dynamics ◽  
Hiv Dynamics

In this paper, a stochastic model with a saturation infection rate representing HIV internal virus dynamics is investigated. We prove that the model exists non-negative solutions. Then we analyse the asymptotic behavior of the model. Finally, numerical simulations are presented to illustrate our mathematical findings.

scholarly journals Analysis of an algorithm catching elephants on the Internet

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Yousra Chabchoub ◽  
Christine Fricker ◽  
Frédéric Meunier ◽  
Danielle Tibi
Keyword(s):  
Asymptotic Behavior ◽  
Markov Chain ◽  
Stochastic Model ◽  
Limit Theorems ◽  
Bloom Filter ◽  
Simplified Model ◽  
The Internet ◽  
Huge Amount ◽  
International Audience ◽  
On Line

International audience The paper deals with the problem of catching the elephants in the Internet traffic. The aim is to investigate an algorithm proposed by Azzana based on a multistage Bloom filter, with a refreshment mechanism (called $\textit{shift}$ in the present paper), able to treat on-line a huge amount of flows with high traffic variations. An analysis of a simplified model estimates the number of false positives. Limit theorems for the Markov chain that describes the algorithm for large filters are rigorously obtained. The asymptotic behavior of the stochastic model is here deterministic. The limit has a nice formulation in terms of a $M/G/1/C$ queue, which is analytically tractable and which allows to tune the algorithm optimally.

scholarly journals Periodic Property and Asymptotic Behavior for a Discrete Ratio-Dependent Food-Chain System with Delays

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Changjin Xu ◽  
Peiluan Li ◽  
Maoxin Liao
Keyword(s):  
Asymptotic Behavior ◽  
Food Chain ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Chain System ◽  
Periodic Property ◽  
Ratio Dependent

In this paper, a discrete ratio-dependent food-chain system with delay is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and the method of Lyapunov function, a set of sufficient conditions for the existence of positive periodic solutions and global asymptotic stability of the model are established.

scholarly journals Does moving up a food chain increase aggregation in parasites?

2016 ◽  
Vol 13 (118) ◽  
pp. 20160102 ◽  
Author(s):  
R. J. G. Lester ◽  
R. McVinish
Keyword(s):  
Stochastic Model ◽  
Trophic Level ◽  
Food Chain ◽  
Feeding Behaviour ◽  
Parasite Species ◽  
Fish Parasites ◽  
Data Points ◽  
Parasite Aggregation ◽  
High Parasite ◽  
Chain Increase

General laws in ecological parasitology are scarce. Here, we evaluate data on numbers of fish parasites published by over 200 authors to determine whether acquiring parasites via prey is associated with an increase in parasite aggregation. Parasite species were grouped taxonomically to produce 20 or more data points per group as far as possible. Most parasites that remained at one trophic level were less aggregated than those that had passed up a food chain. We use a stochastic model to show that high parasite aggregation in predators can be solely the result of the accumulation of parasites in their prey. The model is further developed to show that a change in the predators feeding behaviour with age may further increase parasite aggregation.

scholarly journals Asymptotic behavior of a three-species food chain model with time-varying delays

2021 ◽  
Author(s):  
Yuxiao Zhao ◽  
Linshan Wang ◽  
Yangfan Wang
Keyword(s):  
Asymptotic Behavior ◽  
Exponential Stability ◽  
Positive Solutions ◽  
Food Chain ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Chain Model ◽  
Time Varying ◽  
Razumikhin Technique ◽  
Food Chain Model

In this paper, a stochastic three-species food chain model with time-varying delays is focussed. The existence and the asymptotic behavior of global positive solutions to the model are discussed, and the sufficient conditions for the 1th moment practical exponential stability and the extinction of the model are given by using the Razumikhin technique and Lyapunov method.

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