斑块生境中具有捕食风险的动力系统模型及其数值模拟研究  

Dynamical system model with predation risk in patchy habitats and its numerical simulation research

作　　者：李自珍[1] 高猛[1] 徐彩琳[2] 

机构地区：[1]兰州大学数学系,兰州730000 [2]兰州大学生命科学学院,兰州730000

出　　处：《西北植物学报》2004年第3期430-436,共7页Acta Botanica Boreali-Occidentalia Sinica

基　　金：国家基础研究重大项目前期专项 2 0 0 2 CCA0 0 3 0 0 ;教育部科技重点项目 0 1172 ;高等学校博士学科点专项科研基金项目 2 0 0 2 0 73 0 0 17

摘　　要：从生物的捕食系统出发 ,提出了一种斑块生境中具有异质捕食风险的新机制 ,并构造了一个动力系统模型 .在此模型之上 ,首先研究了扩散对系统稳定性的作用 ,并对系统进行了计算机模拟 .研究发现 :具有不同捕食风险的斑块生境之间的扩散 无论是只有食饵的扩散 ,还是食饵和捕食者共同的扩散 对整个捕食系统所起的作用主要取决于扩散的速率——只有在适中的扩散速率下系统才会稳定 ,如果扩散速率过快 ,则引起系统的强烈振荡 .当只有食饵发生扩散时 ,参数 f的值越小 f代表高捕食风险生境斑块体积占整个系统体积的比例 ,系统越稳定 .在捕食者与食饵同时扩散的时候 ,只有适中或较小的参数 f才可以实现系统的长期稳定 .其次研究了系统中种群空间平均平衡密度随扩散速率增加的变化趋势 .模拟结果表明 :系统中食饵种群的空间平均平衡密度随扩散速率增加而减小 ;捕食者种群平衡密度的变化趋势则取决于系统斑块之间的扩散形式 :只有食饵发生扩散时 ,捕食者种群的空间平衡密度先保持不变 ,然后缓慢下降 ;捕食者与食饵同时扩散的时候 ,捕食者种群平衡密度呈上升趋势 .上述结论是由空间异质的捕食风险所决定的 ,也就是一种下行控制力所限制的结果 .综合以上两个结论 ,认为斑块之间的扩散形式决定了扩散对系统动态的?Starting from natural predation systems,we present a new mechanism involving heterogeneous predation risk,and develop a new dynamical system model in patchy habitats.Firstly,the effect of diffusion on the stability of system is investigated according to numerical simulation.We find that diffusion of only prey or both prey and predator between different patches with different predation risk may stabilize the dynamics,mainly depending on the flow rate.Only a medium flow rate can lead to the stability of the system,too large a rate can cause the system to oscillate strongly.When only prey diffuse,the smaller the parameter f (the proportion of patchy volume with larger predation risk to the total volume),the more stable the system is.If both populations can diffuse,however,only medium and very small f values may stabilize the system.Secondly,the response of spatially averaged equilibrium densities of the system to the increasing of the flow rate is examined.With increasing flow rate,the spatial averaged equilibrium density of prey decrease,while that of predator depends on the pattern of diffusion.For the case of only prey diffusion,it remains unchanged first and then decreases slightly,while it increases for the case of combination as the flow rate increases.Our results are,qualitatively,determined by the spatially heterogeneous mechanism that we proposed,and further regulated by top down forces.Of practical importance,the results reported here indicate that which species diffuse plays a key role in the ways in which diffusion influences the stability and the spatial averaged equilibrium densities of the system response to the flow rates increasing.

关 键 词：斑块生境 捕食风险 扩散 空间平均平衡密度 系统稳定性 

分 类 号：Q948.12[生物学—植物学]