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随机生物种群模型若干性质的研究
  • 项目名称：随机生物种群模型若干性质的研究
  • 项目类别：面上项目
  • 批准号：11171081
  • 申请代码：A011403
  • 项目来源：国家自然科学基金
  • 研究期限：2012-01-01-2015-12-31
  • 项目负责人：王克
  • 依托单位：哈尔滨工业大学
  • 批准年度：2011
中文摘要：

在生物生存环境中，随机现象无处不在，因此研究自然界中随机扰动对生物种群模型的影响具有重要的意义。本项目拟对随机生物种群模型的若干性质进行研究，主要问题包括（1）具有白噪声与有色噪声干扰的n个种群捕食者-食饵系统、竞争系统、互惠系统的全局性质，包括持久性、灭绝性、有界性、依分布稳定性、随机极限环存在性等。（2）几类二维随机生物种群模型的最优捕获问题。（3）具有白噪声干扰与有色噪声干扰的珍稀生物的保护区问题。（4）具有随机效应的n个斑块生物种群模型的全局性质。本项目期望，通过对上述问题的研究，能揭示随机扰动对生物种群发展的影响，进一步为一些重要的实际问题，例如，如何更好的开采可持续利用的生物资源以及如何设置珍稀生物保护区与保护区面积问题，提供建设性意见。本项目的研究不仅可以丰富随机微分方程和种群生物学自身的理论，也能推动相关学科的发展。

中文主题词： 生物种群模型；最优捕获；保护区；稳定性；
英文摘要：

population model；optimal harvesting；protection zone；stability；

英文主题词： population model；optimal harvesting；protection zone；stability；
结论摘要：

在生物生存环境中，随机现象无处不在，因此研究自然界中随机扰动对生物种群模型的影响具有重要的意义。本项目对随机生物种群模型的若干性质进行了研究，得出以下结果（1）具有白噪声与有色噪声干扰的n个种群捕食者-食饵系统、竞争系统、互惠系统的全局性质，包括持久性、灭绝性、有界性、依分布稳定性、随机极限环存在性等。（2）几类二维随机生物种群模型的最优捕获问题。（3）具有白噪声干扰与有色噪声干扰的珍稀生物的保护区问题。（4）具有随机效应的n个斑块生物种群模型的全局性质。本项目的研究对如何更好的开采可持续利用的生物资源以及如何设置珍稀生物保护区与保护区面积问题，提供建设性意见。本项目的研究不仅丰富随机微分方程和种群生物学自身的理论，也能推动相关学科的发展。项目研究期间共发表SCI论文87篇。

成果综合统计
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  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 149
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期刊论文
Asymptotic properties of a stochastic predator-prey system with Holling II functional response
无闭轨Lienard系统Q结构的实现
Stability analysis of a stochastic logistic model with infinite delay
A note on a delay Lotka–Volterra competitive system with random perturbations
A note on stability of stochastic logistic equation
A remark on a stochastic predator–prey system with time delays
Stability of a stochastic logistic model with distributed delay
The optimal harvesting policy for non-autonomous populations with discount
无闭轨Lienard系统20种非Q结构的实现
Stochastic Differential Equations with Multi-Markovian Switching
Graph Theory-Based Approach for Stability Analysis of Stochastic Coupled Systems With Levy Noise on
Dynamics of logistic systems driven by levy noise under regime switching
Dynamical properties of a biological population with a protected area under ecological uncertainty
Dynamics of a stochastic Holling II one-predator two-prey system with jumps
Population dynamical behaviors of stochastic logistic system with jumps
Population dynamical behavior of lotka-volterra cooperative systems with random perturbations
Two types of permanence of a stochastic mutualism model
Dynamics and simulations of a logistic model with impulsive perturbations in a random environment
Stochastic SIR model with jumps
Dynamics of a Leslie–Gower Holling-type II predator–prey system with Lévy jumps
Translation properties of time scales and almost periodic functions
Asymptotic behavior of a stochastic nonautonomous Lotka–Volterra competitive system with impulsive p
Persistence and extinction of a single-species population system in a polluted environment with rand
Numerical simulations and modeling for stochastic biological systems with jumps
Stochastic Lotka-Volterra systems with Levy noise
Global exponential stability for coupled systems of neutral delay differential equations
Existence and uniqueness of m-solutions for backward stochastic volterra integral equations
Asymptotic properties of a stochastic Lotka-Volterra cooperative system with impulsive perturbations
Stochastic SEIR model with jumps
Optimal Harvesting for a Logistic Population Dynamics Driven by a L,vy Process
Parameter-dependent integral on time scales
Exponential Stability of Coupled Systems on Networks with Mixed Delays and Reaction-Diffusion Terms
Razumikhin-type theorems on exponential stability of stochastic functional differential equations on
Can protection zone potentially strengthen protective effects in random environments?
Stochastic Logistic Systems with Jumps
Stability analysis of a stochastic Gilpin-Ayala model driven by Levy noise
Analysis of an improved epidemic model with stochastic disease transmission
Asymptotic behavior of non-autonomous stochastic Gilpin-Ayala competition model with jumps
Stability of stochastic Richards growth model
Stochastic Model for Spread of AIDS Driven by Levy Noise
Optimal harvesting for a stochastic n-dimensional competitive lotka-volterra model with jumps
Almost sure permanence of stochastic single species models
Asymptotic properties of stochastic hybrid Gilpin-Ayala system with jumps
Asymptotic stability of a two-group stochastic SEIR model with infinite delays
Dynamics of a Two-Prey One-Predator System in Random Environments
Asymptotic behavior of stochastic gilpin-ayala mutualism model with jumps
Stationary distribution and stochastic hopf bifurcation for a predator-prey system with noises
Persistence and extinction of a non-autonomous logistic equation with random perturbation
The protection zone for biological population in random environment
Global stochastic stability analysis for stochastic neural networks with infinite delay and Markovia
Dynamical behavior of a competitive system under the influence of random disturbance and toxic subst
Asymptotic boundedness for stochastic coupled systems on networks with Markovian switching
A graph-theoretic approach to stability of neutral stochastic coupled oscillators network with time-
Global exponential stability for coupled retarded systems on networks: A graph-theoretic approach
Analysis of a stochastic autonomous mutualism model
Global stability of coupled nonlinear systems with Markovian switching
Stability and Boundedness of Stochastic Volterra Integrodifferential Equations with Infinite Delay
Effects of Dispersal for a Logistic Growth Population in Random Environments
Synchronization of delayed coupled reaction-diffusion systems on networks
Analysis on a Stochastic Two-Species Ratio-Dependent Predator-Prey Model
Global exponential stability for stochastic networks of coupled oscillators with variable delay
The existence of periodic solutions for coupled systems on networks with time delays
Asymptotic behavior of a stochastic non-autonomous predator-prey model with impulsive perturbations
Graph-theoretic approach to stability of multi-group models with dispersal
DYNAMICAL PROPERTIES OF A STOCHASTIC TWO-SPECIES SCHOENER';S COMPETITIVE MODEL
一个具有随机传染率艾滋病模型的渐近行为
离散时间斑块单种群模型的稳定性分析
随机扰动下的非自治种群的随机持久性
随机微分方程稳定性的新的充分条件
网络上复杂耦合系统的同步
DYNAMICAL PROPERTIES OF A STOCHASTIC TWO-SPECIES SCHOENER＇S COMPETITIVE MODEL
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