Ngonghala Calistus N, Feudel Ulrike, Showalter Kenneth
Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506-6310, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056206. doi: 10.1103/PhysRevE.83.056206. Epub 2011 May 9.
Coupled systems can exhibit an unusual kind of multistability, namely, the coexistence of infinitely many attractors for a given set of parameters. This extreme multistability is demonstrated to occur in coupled chemical model systems with various types of coupling. We show that the appearance of extreme multistability is associated with the emergence of a conserved quantity in the long-term limit. This conserved quantity leads to a "slicing" of the state space into manifolds corresponding to the value of the conserved quantity. The state space "slices" develop as t→∞ and there exists at least one attractor in each of them. We discuss the dependence of extreme multistability on the coupling and on the mismatch of parameters of the coupled systems.
耦合系统可以表现出一种不同寻常的多重稳定性，即对于给定的一组参数，存在无穷多个吸引子共存的情况。这种极端多重稳定性在具有各种耦合类型的耦合化学模型系统中得到了证明。我们表明，极端多重稳定性的出现与长期极限中一个守恒量的出现有关。这个守恒量导致状态空间被“分割”成与守恒量值相对应的流形。随着t→∞，状态空间“切片”不断发展，并且每个切片中至少存在一个吸引子。我们讨论了极端多重稳定性对耦合以及耦合系统参数失配的依赖性。
