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991.
The secant caustic of a planar curve M is the image of the singular set of the secant map of M. We analyze the geometrical properties of the secant caustic of a planar curve, i.e. the number of branches of the secant caustic, the parity of the number of cusps and the number of inflexion points in each branch of this set. In particular, we investigate in detail some of the geometrical properties of the secant caustic of a rosette, i.e. a smooth regular oriented closed curve with non-vanishing curvature. 相似文献
992.
Since intraguild predation (IGP) is a ubiquitous and important community module in nature and Allee effect has strong impact on population dynamics, in this paper we propose a three-species IGP food web model consisted of the IG predator, IG prey and basal prey, in which the basal prey follows a logistic growth with strong Allee effect. We investigate the local and global dynamics of the model with emphasis on the impact of strong Allee effect. First, positivity and boundedness of solutions are studied. Then existence and stability of the boundary and interior equilibria are presented and the Hopf bifurcation curve at an interior equilibrium is given. The existence of a Hopf bifurcation curve indicates that if competition between the IG prey and IG predator for the basal resource lies below the curve then the interior equilibrium remains stable, while if it lies above the curve then the interior equilibrium loses its stability. In order to explore the impact of Allee effect, the parameter space is classified into sixteen different regions and, in each region, the number of interior equilibria is determined and the corresponding bifurcation diagrams on the Allee threshold are given. The extinction parameter regions of at least one species and the necessary coexistence parameter regions of all three species are provided. In addition, we explore possible dynamical patterns, i.e., the existence of multiple attractors. By theoretical analysis and numerical simulations, we show that the model can have one (i.e. extinction of all species), two (i.e. bi-stability) or three (i.e. tri-stability) attractors. It is also found by simulations that when there exists a unique stable interior equilibrium, the model may generate multiple attracting periodic orbits and the coexistence of all three species is enhanced as the competition between the IG prey and IG predator for the basal resource is close to the Hopf bifurcation curve from below. Our results indicate that the intraguild predation food web model exhibits rich and complex dynamic behaviors and strong Allee effect in the basal prey increases the extinction risk of not only the basal prey but also the IG prey or/and IG predator. 相似文献
993.
Pythagorean-hodograph (PH)曲线因其在弧长和等距线计算方面的优势而被广泛应用于曲线建模中.本文讨论了在总弧长约束下的三次PH曲线$G^2$连续拼接问题.具体地说,给定两个端点和一个拼接点,构造两条三次PH曲线,使其在指定总弧长下插值两个端点,并且在连接点处是$G^2$连续的.这也可以看作是一个曲线延拓问题.根据三次PH曲线的弧长公式和$G^2$连续条件,最终将问题转化为了一个带有约束的极小值问题,同时我们给出了几个具体例子来说明该方法. 相似文献
994.
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997.
大多数关于环境库兹涅茨曲线的实证研究隐含地假定地区间环境质量彼此独立,这种对空间相关性的忽视可能导致实证结果的偏误。本文利用2007年中国275个地级及以上城市的数据,对纳入FDI和空间相关性的环境库兹涅茨扩展模型进行了实证检验。研究结果发现:环境库兹涅茨倒U型曲线是否存在很大程度上取决于污染指标以及估计方法的选取;FDI并不一定导致城市环境的恶化;空间相关是影响城市环境质量的重要因素,一个城市的污染物排放受到邻近城市的影响。 相似文献
998.
In this paper we propose a construction method of the planar cubic algebraic spline curve with endpoint interpolation conditions
and a specific analysis of its properties. The piecewise cubic algebraic curve has G
2 continuous contact with the control polygon at two endpoints and is G
2 continuous between each segments of itself. The process of this method is simple and clear, and provides a new way of thinking
to design implicit curves. 相似文献
999.
黄荣培 《纯粹数学与应用数学》2011,27(3):302-307
讨论三维洛仑兹空间形式中的类光曲线粒子模型,研究依赖于粒子轨道的Cartan曲率的作用,找出了沿着极值曲线的Killing场,通过Killing场构造合适的坐标系,用积分求出极值曲线的参数表达式. 相似文献
1000.
It is shown that the curvature function satisfies a nonlinear evolution equation under the general curve shortening flow and
a detailed asymptotic behavior of the closed curves is presented when they contract to a point in finite time. 相似文献