共查询到19条相似文献,搜索用时 78 毫秒
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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. 相似文献
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具Holling第Ⅱ类功能性反应的捕食者--食饵系统的定性分析 总被引:16,自引:2,他引:14
考虑捕食者无密度制约,食饵具有非线性密度制约的第二类Holling功能性反应捕食者-食饵系统。对该系统给出了完整的定性分析,证明了该系统至多有一个极限环,存在极限环的充要条件是平衡点不稳定。 相似文献
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一类Holling功能性反应模型极限环的唯一性 总被引:3,自引:1,他引:2
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… 相似文献
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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. 相似文献
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一类被开发的HollingⅢ类功能反应模型的定性分析 总被引:2,自引:0,他引:2
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. 相似文献
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具有稀疏效应的Predator-Prey模型的分支问题 总被引:4,自引:0,他引:4
讨论了具有稀疏效应的捕食-食饵模型的分支问题,并利用Hopf分支理论和分界线环分支理论,得到了有多个极限环的结果。 相似文献
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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 总被引:2,自引:0,他引:2
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。 相似文献
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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。 相似文献
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We investigate two models of glycolytic oscillations. Each model consists of two coupled nonlinear ordinary differential
equations. Both models are found to have a saddle point at infinity and to exhibit a saddle-node bifurcation at infinity,
giving rise to a second saddle and a stable node at infinity. Depending on model parameters, a stable limit cycle may blow
up to infinite period and amplitude and disappear in the bifurcation, and after the bifurcation, the stable node at infinity
then attracts all trajectories. Alternatively, the stable node at infinity may coexist with either a stable sink (not at infinity)
or a stable limit cycle. This limit cycle may then disappear in a heteroclinic bifurcation at infinity in which the unstable
manifold from one saddle at infinity joins the stable manifold of the other saddle at infinity. These results explain prior
reports for one of the models concerning parameter values for which the system does not admit any physical (bounded) behavior.
Analytic results on the scaling of amplitude and period close to the bifurcations are obtained and confirmed by numerical
computations. Finally, we consider more realistic modified models where all solutions are bounded and show that some of the
features stemming from the bifurcations at infinity are still present.
Received 4 September 1995; received in revised form 18 September 1996 相似文献
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With the dynamic differential equations of Beeler, G. W., and H. Reuter (1977, J. Physiol. [Lond.]. 268:177-210), we have studied the oscillatory behavior of the ventricular muscle fiber stimulated by a depolarizing applied current I app. The dynamic solutions of BR equations revealed that as I app increases, a periodic repetitive spiking mode appears above the subthreshold I app, which transforms to a periodic spiking-bursting mode of oscillations, and finally to chaos near the suprathreshold I app (i.e., near the termination of the periodic state). Phase resetting and annihilation of repetitive firing in the ventricular myocardium were demonstrated by a brief current pulse of the proper magnitude applied at the proper phase. These phenomena were further examined by a bifurcation analysis. A bifurcation diagram constructed as a function of I app revealed the existence of a stable periodic solution for a certain range of current values. Two Hopf bifurcation points exist in the solution, one just above the lower periodic limit point and the other substantially below the upper periodic limit point. Between each periodic limit point and the Hopf bifurcation, the cell exhibited the coexistence of two different stable modes of operation; the oscillatory repetitive firing state and the time-independent steady state. As in the Hodgkin-Huxley case, there was a low amplitude unstable periodic state, which separates the domain of the stable periodic state from the stable steady state. Thus, in support of the dynamic perturbation methods, the bifurcation diagram of the BR equation predicts the region where instantaneous perturbations, such as brief current pulses, can send the stable repetitive rhythmic state into the stable steady state. 相似文献
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Neurophysiological and anatomical observations are used to derive a non-linear delay-differential equation for the pupil light
reflex with negative feedback. As the gain or the time delay in the reflex is increased, a supercritical Hopf bifurcation
occurs from a stable fixed point to a stable limit cycle oscillation in pupil area. A Hopf bifurcation analysis is used to
determine the conditions for instability and the period and amplitude of these oscillations. The more complex waveforms typical
of the occurrence of higher order bifurcations were not seen in numerical simulations of the model. This model provides a
general framework to study the different types of dynamical behaviors which can be produced by the pupil light reflex, e.g.
edge-light pupil cycling. 相似文献
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The asymptotic behavior of a tri-trophic food chain model is studied. The analysis is carried out numerically, by finding
both local and global bifurcations of equilibria and limit cycles. The existence of transversal homoclinic orbits to a limit
cycle is shown. The appearance of homoclinic orbits, by moving through a homoclinic bifurcation point, is associated with
the sudden disappearance of a chaotic attractor. A homoclinic bifurcation curve, which bounds a region of extinction, is continued
through a two-dimensional parameter space. Heteroclinic orbits from an equilibrium to a limit cycle are computed. The existence
of these heteroclinic orbits has important consequences on the domains of attraction. Continuation of non-transversal heteroclinic
orbits through parameter space shows the existence of two codimension-two bifurcations points, where the saddle cycle is non-hyperbolic.
The results are summarized by dividing the parameter space in subregions with different asymptotic behavior.
Received: 25 February 1998 / Revised version: 19 August 1998 相似文献
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Oscillatory dynamics in rock-paper-scissors games with mutations 总被引:1,自引:0,他引:1
Mauro Mobilia 《Journal of theoretical biology》2010,264(1):1-4226
We study the oscillatory dynamics in the generic three-species rock-paper-scissors games with mutations. In the mean-field limit, different behaviors are found: (a) for high mutation rate, there is a stable interior fixed point with coexistence of all species; (b) for low mutation rates, there is a region of the parameter space characterized by a limit cycle resulting from a Hopf bifurcation; (c) in the absence of mutations, there is a region where heteroclinic cycles yield oscillations of large amplitude (not robust against noise). After a discussion on the main properties of the mean-field dynamics, we investigate the stochastic version of the model within an individual-based formulation. Demographic fluctuations are therefore naturally accounted and their effects are studied using a diffusion theory complemented by numerical simulations. It is thus shown that persistent erratic oscillations (quasi-cycles) of large amplitude emerge from a noise-induced resonance phenomenon. We also analytically and numerically compute the average escape time necessary to reach a (quasi-)cycle on which the system oscillates at a given amplitude. 相似文献
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El Abdllaoui A Auger P Kooi BW Bravo de la Parra R Mchich R 《Mathematical biosciences》2007,210(1):335-354
We consider a predator-prey model in a two-patch environment and assume that migration between patches is faster than prey growth, predator mortality and predator-prey interactions. Prey (resp. predator) migration rates are considered to be predator (resp. prey) density-dependent. Prey leave a patch at a migration rate proportional to the local predator density. Predators leave a patch at a migration rate inversely proportional to local prey population density. Taking advantage of the two different time scales, we use aggregation methods to obtain a reduced (aggregated) model governing the total prey and predator densities. First, we show that for a large class of density-dependent migration rules for predators and prey there exists a unique and stable equilibrium for migration. Second, a numerical bifurcation analysis is presented. We show that bifurcation diagrams obtained from the complete and aggregated models are consistent with each other for reasonable values of the ratio between the two time scales, fast for migration and slow for local demography. Our results show that, under some particular conditions, the density dependence of migrations can generate a limit cycle. Also a co-dim two Bautin bifurcation point is observed in some range of migration parameters and this implies that bistability of an equilibrium and limit cycle is possible. 相似文献
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As the maximal K+-conductance (or K+-channel density) of the Hodgkin-Huxley equations is reduced, the stable resting membrane potential bifurcates at a subcritical Hopf bifurcation into small amplitude unstable oscillations. These small amplitude solutions jump to large amplitude periodic solutions that correspond to a repetitive discharge of action potentials. Thus the specific channel density can act as a bifurcation parameter, and can control the excitability and autorhythmicity of excitable membranes. 相似文献
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We consider the dynamics of the standard model of 3 species competing for 3 essential (non-substitutable) resources in a chemostat
using Liebig's law of the minimum functional response. A subset of these systems which possess cyclic symmetry such that its
three single-population equilibria are part of a heteroclinic cycle bounding the two-dimensional carrying simplex is examined.
We show that a subcritical Hopf bifurcation from the coexistence equilibrium together with a repelling heteroclinic cycle
leads to the existence of at least two limit cycles enclosing the coexistence equilibrium on the carrying simplex- the ``inside'
one is an unstable separatrix and the ``outside' one is at least semi-stable relative to the carrying simplex. Numerical
simulations suggest that there are exactly two limit cycles and that almost every positive solution approaches either the
stable limit cycle or the stable coexistence equilibrium, depending on initial conditions. Bifurcation diagrams confirm this
picture and show additional features. In an alternative scenario, we show that the subcritical Hopf together with an attracting
heteroclinic cycle leads to an unstable periodic orbit separatrix.
This research was partially supported by NSF grant DMS 0211614. KY 40292, USA.
This author's research was supported in part by NSF grant DMS 0107160 相似文献
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The stability properties of the first two time-periodic solutions bifurcating from an unstable uniform steady-state are analyzed
for a model chemical system subject to zero fluxes at the boundaries. The existence of new (secondary) bifurcation points
is investigated on the small amplitude solutions and calculated analytically in the limit of small diffusion coefficients. 相似文献