Zelnik Yuval R, Gandhi Punit, Knobloch Edgar, Meron Ehud
Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, CNRS and Paul Sabatier University, 09200 Moulis, France.
Mathematical Biosciences Institute, Ohio State University, Columbus, Ohio 43210, USA.
Chaos. 2018 Mar;28(3):033609. doi: 10.1063/1.5018925.
Many ecosystems show both self-organized spatial patterns and multistability of possible states. The combination of these two phenomena in different forms has a significant impact on the behavior of ecosystems in changing environments. One notable case is connected to tristability of two distinct uniform states together with patterned states, which has recently been found in model studies of dryland ecosystems. Using a simple model, we determine the extent of tristability in parameter space, explore its effects on the system dynamics, and consider its implications for state transitions or regime shifts. We analyze the bifurcation structure of model solutions that describe uniform states, periodic patterns, and hybrid states between the former two. We map out the parameter space where these states exist, and note how the different states interact with each other. We further focus on two special implications with ecological significance, breakdown of the snaking range and complex fronts. We find that the organization of the hybrid states within a homoclinic snaking structure breaks down as it meets a Maxwell point where simple fronts are stationary. We also discover a new series of complex fronts between the uniform states, each with its own velocity. We conclude with a brief discussion of the significance of these findings for the dynamics of regime shifts and their potential control.
许多生态系统既呈现出自组织空间模式，又具有多种可能状态的多重稳定性。这两种现象以不同形式结合，对变化环境中生态系统的行为有着重大影响。一个显著的例子与两种不同的均匀状态以及模式化状态的三稳态有关，这一现象最近在旱地生态系统的模型研究中被发现。通过一个简单模型，我们确定了参数空间中三稳态的范围，探究其对系统动力学的影响，并考虑其对状态转变或 regime 转移的意义。我们分析了描述均匀状态、周期性模式以及前两者之间混合状态的模型解的分岔结构。我们绘制出这些状态存在的参数空间，并指出不同状态之间是如何相互作用的。我们进一步关注具有生态意义的两个特殊影响，即蜿蜒范围的崩溃和复杂前沿。我们发现，同宿蜿蜒结构内混合状态的组织在遇到简单前沿静止的麦克斯韦点时会崩溃。我们还发现了均匀状态之间的一系列新的复杂前沿，每个前沿都有其自身的速度。最后，我们简要讨论了这些发现对 regime 转移动力学及其潜在控制的意义。
