食饵具有存放周期性制约的捕食者-食饵系统模型及其动态行为的数值模拟研究

基于对自然界捕食系统实际情况的分析出发。对模型进行了扩展，并建立了受时变环境周期激励、食饵具有常数存放率以及食饵具有周期存放等情况下的捕食者--食饵系统的新模型，通过模拟计算相平面轨线(迹)、时程图、极限集状态、截面、功率谱等若干系统指标，分析研究了几个新捕食模型随参数变化时表现出的动态行为以及行为所发生的质的变化．结果表明周期激励强度、食饵常数存放率的大小、食饵周期存放以及周期存放的频度对系统行为都有很大的影响，当食饵存放率为零时，系统随周期激励强度的增大经历了稳定、周期波动、准周期波动和灭绝四种状态；当周期激励强度和频度恒定时，系统随食饵常数存放率的增大经历了周期(准周期)波动、分岔后的周期(准周期)波动和灭绝等状态；而在周期激励强度和频度恒定时，食饵周期存放可能引起系统出现混沌行为；当周期存放的强度较大时，食饵存放频度的变小不利于系统的稳定．

Periodically restricted predator-prey model with investing for prey group and its numerical simulations

Starting from an analysis on real predator- prey systems in the natural world,this paper has developed new predation system models with periodic restrictions by time- varying environment,constant or periodic feeding on prey species by expanding Lotka- Volterra model.Also,it has examined the varia- tions of dynamical behaviors of new models with different parameter values via computing and drawing several indexes of system,such as trajectories,population size with time,asymptotic states,section and power spectrum.The simulation results show that the strength of periodic restrictions and the strength and frequency of feeding on prey species have significant influences on the dynamical behaviors of preda- tor- prey systems.When the feeding rate is constant,the system goes from stable states through periodic ( anti- periodic) fluctuations to extinction as the strength of periodic restriction increases.With the increasing of constant feeding rate,the system goes through periodic( anti- periodic) fluctuations,periodic ( anti- periodic) fluctuations after bifurcation and extinction while the strength and frequency of periodic restrictions are both constant.Interestingly,periodic feeding might lead to chaotic dynamics.In addition, if the strength of periodic feeding is large,the frequency of periodic feeding changing low destabilizes the system.