scholarly journals Stochastic Delay Population Dynamics under Regime Switching: Permanence and Asymptotic Estimation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zheng Wu ◽  
Hao Huang ◽  
Lianglong Wang
Keyword(s):  
Population Dynamics ◽  
Random Environment ◽  
Regime Switching ◽  
Matrix Method ◽  
Volterra Model ◽  
Function Technique ◽  
Stochastic Delay ◽  
Switching Diffusion ◽  
Asymptotic Estimation ◽  
Diffusion In Random Environment

This paper is concerned with a delay Lotka-Volterra model under regime switching diffusion in random environment. Permanence and asymptotic estimations of solutions are investigated by virtue of V-function technique, M-matrix method, and Chebyshev's inequality. Finally, an example is given to illustrate the main results.

scholarly journals Stochastic Delay Population Dynamics under Regime Switching: Global Solutions and Extinction

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Zheng Wu ◽  
Hao Huang ◽  
Lianglong Wang
Keyword(s):  
Regime Switching ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Volterra Model ◽  
Ultimate Boundedness ◽  
Stochastic Delay ◽  
Switching Diffusion ◽  
Diffusion In Random Environment ◽  
Stochastically Ultimate Boundedness ◽  
Generalized Itô Formula

This paper is concerned with a delay Lotka-Volterra model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall inequality and Young’s inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Finally, an example is given to illustrate the main results.

scholarly journals Stochastic Delay Logistic Model under Regime Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Zheng Wu ◽  
Hao Huang ◽  
Lianglong Wang
Keyword(s):  
Regime Switching ◽  
Logistic Model ◽  
Sufficient Conditions ◽  
Function Technique ◽  
Stochastic Permanence ◽  
Stochastic Delay ◽  
Gronwall’S Inequality ◽  
Diffusion In Random Environment ◽  
Stochastically Ultimate Boundedness ◽  
Generalized Itô Formula

This paper is concerned with a delay logistical model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall's inequality, and Young's inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Also, the relationships between the stochastic permanence and extinction as well as asymptotic estimations of solutions are investigated by virtue ofV-function technique,M-matrix method, and Chebyshev's inequality. Finally, an example is given to illustrate the main results.

scholarly journals Least Squares Estimation for Discretely Observed Stochastic Lotka–Volterra Model Driven by Small α -Stable Noises

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Chao Wei ◽  
Yan Wei ◽  
Yingying Zhou
Keyword(s):  
Population Dynamics ◽  
Least Squares ◽  
Random Environment ◽  
Schwarz Inequality ◽  
Volterra Model ◽  
Markov Inequality ◽  
Numerical Examples ◽  
Model Driven ◽  
Gronwall’S Inequality ◽  
Least Squares Estimators

Stochastic Lotka–Volterra model driven by small α -stable noises is used to describe population dynamics perturbed by random environment. However, parameters in the model are always unknown. The contrast function is given to obtain least squares estimators. The consistency and the rate of convergence of the least squares estimators are proved, and the asymptotic distribution of the estimators are derived by Markov inequality, Cauchy–Schwarz inequality, and Gronwall’s inequality. Some numerical examples are provided to verify the effectiveness of the estimators.

scholarly journals Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Qiaoqin Gao ◽  
Zhijiang Luo ◽  
Guirong Liu
Keyword(s):  
Numerical Simulations ◽  
Existence And Uniqueness ◽  
Matrix Method ◽  
Lyapunov Method ◽  
Markovian Switching ◽  
Dynamics Analysis ◽  
Stochastic Permanence ◽  
Stochastic Delay ◽  
Global Positive Solution ◽  
Theoretical Results

This paper considers a stochastic delay Gilpin-Ayala model with Markovian switching. Using Lyapunov method, we show existence and uniqueness of global positive solution. Then, by using Chebyshev’s inequality, M-matrix method, and BDG’s inequality, stochastic permanence and asymptotic estimations of solutions are studied. Finally, numerical simulations illustrate the theoretical results. Our results generalize and improve the existing results.

scholarly journals Inadequate Sampling Rates Can Undermine the Reliability of Ecological Interaction Estimation

2019 ◽  
Vol 24 (2) ◽  
pp. 48
Author(s):  
Brenno Cabella ◽  
Fernando Meloni ◽  
Alexandre S. Martinez
Keyword(s):  
Population Dynamics ◽  
Slow Rate ◽  
Data Interpretation ◽  
Volterra Model ◽  
Population Cycle ◽  
Cycle Period ◽  
Oscillatory Regime ◽  
Ecological Interaction ◽  
Effect Relationship ◽  
Acquisition Rates

Cycles in population dynamics are abundant in nature and are understood as emerging from the interaction among coupled species. When sampling is conducted at a slow rate compared to the population cycle period (aliasing effect), one is prone to misinterpretations. However, aliasing has been poorly addressed in coupled population dynamics. To illustrate the aliasing effect, the Lotka–Volterra model oscillatory regime is numerically sampled, creating prey–predator cycles. We show that inadequate sampling rates may produce inversions in the cause-effect relationship among other artifacts. More generally, slow acquisition rates may distort data interpretation and produce deceptive patterns and eventually leading to misinterpretations, as predators becoming preys. Experiments in coupled population dynamics should be designed that address the eventual aliasing effect.

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