共查询到19条相似文献,搜索用时 156 毫秒
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研究一类具有时滞和阶段结构的捕食模型的稳定性和Hopf分支.以滞量为参数,得到了系统正平衡点的稳定性和Hopf分支存在的充分条件.利用规范型和中心流形定理,给出了确定Hopf分支方向和分支周期解的稳定性的计算公式. 相似文献
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一类具有时滞和Holling Ⅲ型功能性反应的捕食模型的稳定性和Hopf分支 总被引:1,自引:0,他引:1
研究一类具有时滞和Holling Ⅲ型功能性反应的捕食模型的稳定性和Hopf分支.以滞量为参数,得到了系统正平衡点的稳定性和Hopf分支存在的充分条件,给出了确定Hopf分支方向和分支周期解的稳定性的计算公式. 相似文献
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研究一类微气泡耦合时滞系统的稳定性以及Hopf分支,得到了稳定性和Hopf分支出现的条件,并利用泛函微分方程相关理论讨论出分支周期解的分支方向、稳定性和分支周期的变化律. 相似文献
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研究一类具有混沌同步的Lorenz时滞系统在零平衡点处的稳定性以及Hopf分支,得到了系统的稳定性稳定性开关和Hopf分支出现的条件,并讨论出分支周期解的分支方向、稳定性和分支周期的变化律.最后,做了一些数值以验证理论分析的正确性,并模拟出正平衡点产生稳定的周期解. 相似文献
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本文研究一类带有分段常数变量的Lorenz系统的稳定性和分支行为.首先通过计算转化得到Lorenz系统对应的差分系统,利用线性稳定性理论讨论平衡点局部渐近稳定的充要条件.其次选择差分系统三个参数的一个参数为分支参数,利用分支理论研究平衡点处产生Neimark-Sacker分支不变闭曲线的充要条件,并使用分支理论给出判断分支不变闭曲线的稳定性的阈值.最后数值模拟验证了理论分析的正确性. 相似文献
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《数学的实践与认识》2013,(21)
研究化学中一类时滞自催化反应扩散方程在Neumann边值条件下的稳定性和Hopf分支,得到了稳定性和Hopf分支出现的条件,并利用中心流形和规范型理论讨论其分支周期解的分支方向和稳定性及分支周期的交化律. 相似文献
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以滞量τ为分支参数,研究了具时滞的能源价格模型的动力学行为,这些行为包括:系统在平衡点附近的稳定性,局部Hopf分支的存在性,发生条件.Hopf分支的方向,分支周期解的稳定性以及分支随参数变化其周期解的周期变化.最后通过数值模拟验证了理论分析结果,并用分支理论解释了能源价格模型产生且维持周期振荡的原因. 相似文献
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蛙卵有丝分裂模型的鞍结点不变圈及其分支 总被引:1,自引:1,他引:0
本文对Borisuk MT和Tyson JJ在[1]中所提出的一个有关蛙卵有丝分裂的平面三次系统模型证明了鞍结点不变圈的存在性,给出了鞍结点不变圈所在的空间区域和所对应的参数区域,所得结果严格地证明了[1]中给出的数值结果。此外,我们还给出了从此鞍结点不变圈分支出极限环的条件。 相似文献
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In this paper, we investigate the dynamics in a class of discrete-time neuron mod-els. The neuron model we discussed, defined by such periodic input-output mapping as a sinusoidal function, has a remarkably larger memory capacity than the conven-tional association system with the monotonous function. Our results show that the orbit of the model takes a conventional bifurcation route, from stable equilibrium, to periodicity, even to chaotic region. And the theoretical analysis is verified by numerical simula... 相似文献
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Wei Guoqiang 《Annals of Differential Equations》2006,22(4):573-581
In this paper, we consider the bifurcation for a class of cubic integrable system under cubic perturbation. Using bifurcation theory and qualitative analysis, we obtain a complete bifurcation diagram of the system in a neighbourhood of the origin for parameter plane. 相似文献
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本文利用Lyapunov-Schmidt方法对一类群S4对称的自治系统进行讨论,得到了Hopf分支解的存在条件,研究了分支解的结构。 相似文献
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Xuanliang Liu 《Applied mathematics and computation》2011,218(5):2300-2309
A predator-prey system with disease in the prey is considered. Assume that the incidence rate is nonlinear, we analyse the boundedness of solutions and local stability of equilibria, by using bifurcation methods and techniques, we study Bogdanov-Takens bifurcation near a boundary equilibrium, and obtain a saddle-node bifurcation curve, a Hopf bifurcation curve and a homoclinic bifurcation curve. The Hopf bifurcation and generalized Hopf bifurcation near the positive equilibrium is analyzed, one or two limit cycles is also discussed. 相似文献
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Abstract The present paper deals with a detritus‐based food‐chain model within a mangrove ecosystem. The top predator (mainly fish) is assumed to have a commercial value and undergoes harvesting. Stability and bifurcation behavior of the model is studied and a threshold harvest rate is obtained. Next we introduce environmental nonhomogenity into the model equation. The resulting reaction diffusion system is investigated, and the criteria for supercritical Hopf bifurcation is obtained using the method of Lyapunov first coefficient. A comparison of the critical harvest rates under the homogeneous and the nonhomogeneous context is performed both analytically and numerically. 相似文献
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Stability and Hopf bifurcation of a delayed predator-prey system with nonlocal competition and herd behaviour
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In this paper, we investigate the stability and Hopf bifurcation of a diffusive predator-prey system with herd behaviour. The model is described by introducing both time delay and nonlocal prey intraspecific competition. Compared to the model without time delay, or without nonlocal competition, thanks to the together action of time delay and nonlocal competition, we prove that the first critical value of Hopf bifurcation may be homogenous or non-homogeneous. We also show that a double-Hopf bifurcation occurs at the intersection point of the homogenous and non-homogeneous Hopf bifurcation curves. Furthermore, by the computation of normal forms for the system near equilibria, we investigate the stability and direction of Hopf bifurcation. Numerical simulations also show that the spatially homogeneous and non-homogeneous periodic patters. 相似文献