Krawiecki A, Matyjaśkiewicz S
Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 2):036216. doi: 10.1103/PhysRevE.64.036216. Epub 2001 Aug 28.
Blowout bifurcations are investigated in a symmetrized extension of the replacement method of chaotic synchronization which consists of coupling chaotic systems via mutually shared variables. The coupled systems are partly linear with respect to variables that are not shared, and that form orthogonal invariant manifolds in the composite system. If the coupled systems are identical, marginal (projective) synchronization between them occurs. Breaking the symmetry by a small variation of the system parameters leads to a new kind of blowout bifurcation in which the transverse stability is exchanged between the orthogonal invariant manifolds. This bifurcation is neither supercritical nor subcritical. The latter scenarios are also observed as the parameters are further varied, leading to on-off intermittency and the appearance of riddled basins of attraction. Examples using well-known chaotic models are presented.
在混沌同步替换方法的对称扩展中研究了爆裂分岔，该方法通过相互共享的变量耦合混沌系统。耦合系统对于非共享变量部分线性，并且这些变量在复合系统中形成正交不变流形。如果耦合系统相同，则它们之间会出现边缘（投影）同步。通过系统参数的微小变化打破对称性会导致一种新的爆裂分岔，其中正交不变流形之间会交换横向稳定性。这种分岔既不是超临界的也不是亚临界的。随着参数进一步变化，也会观察到后一种情况，导致开-关间歇性和吸引子的迷宫状盆地的出现。给出了使用著名混沌模型的示例。
