Essentially asymptotically stable homoclinic networks
Essentially asymptotically stable homoclinic networks
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本质上渐近稳定的同宿网络
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
A. J. Homburg
中科院分区：
文献类型：
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作者：
R. Driesse;A. J. Homburg
墨尔本[非渐进稳定吸引子的一个例子，非线性4（3）（1991），pp. 835-844]讨论了一个鲁棒异宿网络的例子，该网络不是渐近稳定的，但具有称为本质渐近稳定的强吸引特性。我们确定这种现象对于同宿网络是可能的，其中所有异宿轨迹都是对称相关的。此外，我们还研究了从渐近稳定到本质渐近稳定的同宿网络的横向分支。基本渐近稳定的同宿网络原来吸引所有附近的点，除了那些在同宿网络之外的余维一稳定平衡流形上的点。
Melbourne [An example of a nonasymptotically stable attractor, Nonlinearity 4(3) (1991), pp. 835–844] discusses an example of a robust heteroclinic network that is not asymptotically stable but which has the strong attracting property called essential asymptotic stability. We establish that this phenomenon is possible for homoclinic networks, where all heteroclinic trajectories are symmetry related. Moreover, we study a transverse bifurcation from an asymptotically stable to an essentially asymptotically stable homoclinic network. The essentially asymptotically stable homoclinic network turns out to attract all nearby points except those on codimension-one stable manifolds of equilibria outside the homoclinic network.