一类被开发的HollingⅢ类功能反应模型的定性分析

本文研究了一类捕食种群、食饵种群同时具有收获率的HollingⅢ类功能反应生态系统,其中食饵种群具有非线性密度制约,捕食者无密度制约.应用微分方程定性理论讨论了系统的平衡点,分析了中心焦点的阶数以及稳定性,所给定参数满足一定条件时系统不存在极限环,最后根据细焦点的稳定性判断出极限环的存在性,并验证了极限环的惟一性.     

具功能性反应函数kxθ的捕-食系统极限环的存在唯一性

研究了捕食者无密度制约,食饵具有功能性反函数kx~θ(0＜θ≤1)的捕-食系统的定性行为．在食饵有(或无)常数放养率的情况下,利用Pioncare-Bendixsion环域定理,极限环的存在唯一性定理及旋转向量场理论,对此系统作了完整的定性分析,得到了该系统全局渐近稳定和存在唯一稳定极限环的充分条件．     

双密度制约的Holling Ⅱ型捕食动力系统的定性分析

研究食饵具有非线性密度制约捕食者具有线性密度制约的HollingⅡ型捕食动力系统．以食饵的环境容纳量为分支参数,由Hopf分支得到小振幅极限环的存在性,同时也得到了正平衡点的全局稳定性和非小振幅极限环的存在唯一性的充分条件．     

一类具有HollingⅡ类功能反应且两种群均有密度制约项的捕食系统极…

本文研究了具有ＨｏｌｌｉｎｇⅡ类功能性反应,食饵,捕食者均有密度制约项的一类捕食生态系统唯一极限环的条件。     

一类具有HollingⅡ类功能反应且两种群均有密度制约项的捕食系统极限环的唯一

本文研究了具有HollingⅡ类功能性反应、食饵、捕食者均有密度制约项的一类捕食生态系统存在唯一极限环的条件．     

一类具有非单调增长率和功能反应的捕食者-食饵系统的定性分析

考虑一类食饵密度具有非单调增长率,捕食者具有功能性反应的捕食者一食饵系统。得到系统在第一象限内正平衡点的区域稳定的条件和极限环存在唯一的条件,完整地讨论了系统(1)的拓扑结构。     

一类Holling功能性反应模型极限环的唯一性

考虑功能性反应的捕食-食饵模型这里y表示捕食者种群的密度,当a-（22）≠0时它具有线性密度制约,x表示食饵种群密度,当φ（x）≡ax/（1＋ωx）时称（1）为第二类功能性反应模型．文〔1〕研究了捕食者没有密度制约（对应于a_（22）=0）、食饵具有线性密度制约(对应于g（x）=b_1-a_(11)x）的Ⅱ类功能性反应模型（1）,得到了极限环存在性及唯一性的完整结论．最近文〔2〕在a_(22)≠O的条件下讨论了系统(1),得到了极限环的存在性与不存在性等福建省自然科学基金和国家自然科学基金资助项目（19371069号）．本文第一作者现为浙江大学访问学…     

一类具HOllingⅡ类功能性反应且存在两个极限环的捕食系统的定性分析

本文在文献[1]的基础上对具有HollingⅡ类功能性反应,且食饵、捕食者两种群均具有密度制约的食饵-捕食者生态系统（E）的定性结构进行了进一步的分析,得到（E）存在唯一正平衡点的充要条件,进而在此条件下,对（E）进行全面的定性分析,特别地证明了在一定条件下,系统（E）在其唯一正平衡点外围至少存在两个极限环。     

一类食饵具有常数收获率和Holling Ⅲ型功能性反应的捕食者-食饵模型的定性分析

本文对捕食者种群、食饵种群均在线性密度制约的条件下,食饵种群具有常数收获率的HollingⅢ型功能性反应模型进行定性分析,通过运用定性分析的方法和利用Dulac函数方法,分别讨论了模型正平衡点稳定性、极限环的存在性以及无穷远奇点的稳定性,得到了正平衡点存在的条件和在其周围不存在极限环的条件,以及无穷远点的性态,并给出了模型轨线的全局结构图.最后,对该模型作了数值的仿真模拟验证.     

具有Holling-Ⅳ功能反应的周期捕食者非密度制约的捕食食饵模型的持久性和灭绝性（英文）

本文研究了一类具有功能反应周期的捕食食饵模型,其中捕食者是非密度制约的.我们得到使系统持久灭绝,周期解存在的积分形式的充分条件.把一些关于捕食者密度制约的重要的结论推广到了捕食者非密度制约的情形.     

Oscillations in Controlled Biochemical Systems

Stability analysis of equations describing certain biochemical control mechanisms involving negative feedback suggests that limit cycle behavior might be possible if the control system involves a sufficient number of intermediate chemical steps. For the example considered in this paper, digital simulation of the non-linear control system illustrates that limit cycle behavior actually arises for a sixth-order system. On the other hand, the corresponding fourth- and fifth-order systems are asymptotically stable.     

具非线性饱和功能反应的捕食者-食饵系统的定性分析

研究了一类具有非线性饱和功能反应的捕食者—食饵系统的定性行为.结果表明:当正平衡点稳定时,系统为全局渐近稳定的;当正平衡点不稳定时,系统存在唯一稳定的极限环.     

一类非线性微分动力系统的定性分析

本文研究了一类非线性微分动力系统０,ｂ＞０,Ｐ＞０）的定性行为,完整地解决了系统的极限环的不存在性、存在性和唯一性问题。得到系统有唯一极限环当且仅当（Ｐ一１）ａ－ｂ＞（ａ＋ｂ）~（Ｐ＋１）     

Neural dynamics under noise in the olfactory system

A study is made of the dynamical properties of mammalian olfactory bulb which is represented by a set of nonlinear differential equations. It is shown that when the system of the periglomerular population receives a stationary independent stochastic input from the primary olfactory nerves, the level of ongoing mean pulse rate depends only on the expected value of the input. It is also shown that if the mitral-tufted and granule population receives stationary independent stochastic inputs both from the primary olfactory nerves and centrifugal axons, then there exists a limit cycle detectable in the EEG and the phase of the limit cycle depends only on the expected values of the inputs.     

Modeling experimental time series with ordinary differential equations

Recently some methods have been presented to extract ordinary differential equations (ODE) directly from an experimental time series. Here, we introduce a new method to find an ODE which models both the short time and the long time dynamics. The experimental data are represented in a state space and the corresponding flow vectors are approximated by polynomials of the state vector components. We apply these methods both to simulated data and experimental data from human limb movements, which like many other biological systems can exhibit limit cycle dynamics. In systems with only one oscillator there is excellent agreement between the limit cycling displayed by the experimental system and the reconstructed model, even if the data are very noisy. Furthermore, we study systems of two coupled limit cycle oscillators. There, a reconstruction was only successful for data with a sufficiently long transient trajectory and relatively low noise level.     

Coexistence of two microbial populations competing for a renewable resource in a non-predator-prey system

If two microbial populations compete for a single resource in a homogeneous environment with time invariant inputs they cannot coexist indefinitely if the resource competed for is not renewed by biological activity within the system. Mathematical studies have shown that in a predator-prey system, where the resource (prey) is self-renewing, the two competitors (predators) can coexist in a limit cycle. This suggests that if the resource competed for is renewed by biological activity within the system coexistence can occur in any microbial system provided that it exhibits the same features as, but without being, a predator-prey one. A food chain involving commensalism, competition and amensalism is presented here. Two subcases are considered. It is only when maintenance effects are taken into account that coexistence, in limit cycles, can occur for this system. Limit cycle solutions for the system are demonstrated with the help of computer simulations. Some necessary conditions for coexistence are presented, as are some speculations regarding the possible physical explanations of the results.     

Coevolution can stabilize a mutualistic interaction

Interspecific mutualisms are ubiquitous in nature, despite their ecological and evolutionary instability. Recent studies have developed coevolutionary theory of mutualisms, which coupled population and evolutionary dynamics, to resolve the longstanding puzzle. However, earlier studies assumed a time-scale separation between these dynamics, leaving an unanswered question of how a relaxation in the time-scale separation affects the coevolutionary dynamics of mutualism. Here I relax the strong assumption to theoretically show that ecological and evolutionary dynamics occurring in a similar time scale can stabilize an otherwise unstable mutualism. I show that the coevolutionary dynamics can cause a stable limit cycle or stable equilibrium in the population sizes, even if the population sizes increase unbounded in the absence of evolutionary adaptation. In contrast, coevolution can also cause stable limit cycle even if the population dynamics is stable in the absence of evolutionary adaptation. Furthermore, the model predicts that the population dynamics is likely to converge to equilibrium when the evolutionary speed of two species is similar and fast or highly dissimilar. The results suggest that the ease of the evolutionary ‘arms race’ is of crucial importance to maintain mutualism.     

具有食饵自身抑制作用的Volterra方程的极限环解

一、引言 在捕食者与食饵相互作用的生态数学模型中,比较典型的是Volterra模型(E.C.皮洛,1978)     

Dynamics from a time series: can we extract the phase resetting curve from a time series?

Recordings of the membrane potential from a bursting neuron were used to reconstruct the phase curve for that neuron for a limited set of perturbations. These perturbations were inhibitory synaptic conductance pulses able to shift the membrane potential below the most hyperpolarized level attained in the free running mode. The extraction of the phase resetting curve from such a one-dimensional time series requires reconstruction of the periodic activity in the form of a limit cycle attractor. Resetting was found to have two components. In the first component, if the pulse was applied during a burst, the burst was truncated, and the time until the next burst was shortened in a manner predicted by movement normal to the limit cycle. By movement normal to the limit cycle, we mean a switch between two well-defined solution branches of a relaxation-like oscillator in a hysteretic manner enabled by the existence of a singular dominant slow process (variable). In the second component, the onset of the burst was delayed until the end of the hyperpolarizing pulse. Thus, for the pulse amplitudes we studied, resetting was independent of amplitude but increased linearly with pulse duration. The predicted and the experimental phase resetting curves for a pyloric dilator neuron show satisfactory agreement. The method was applied to only one pulse per cycle, but our results suggest it could easily be generalized to accommodate multiple inputs.