Exploring instability in complex systems - simulations in no-man's land

预测和分析复杂系统和模型中的突变（称为倾翻）是当前科学界的一个主题，也是一个紧迫的社会问题。一些引起激烈争论的例子包括墨西哥湾流可能的崩溃、营养物污染的湖泊中植被的突然丧失，或者干旱地区植被状态和沙漠状态之间的变化。虽然这些情况下的小费是很好地理解在理想化的数学模型，他们的分析受到限制，在现场观察，实验室实验和复杂的模型模拟的不可能系统地探讨动态不稳定的现象。对于许多复杂系统，平衡的概念仅在统计力学意义上被定义为一种新兴现象，根据其定义，它必须是稳定的。拟议的研究将开发通用数学方法，以消除这些限制：它们将使实验者和建模者能够发现和跟踪实验室实验和复杂模型模拟中的不稳定现象，或者，更一般地说，在任何情况下，可以根据系统的真实的输出向系统提供输入。有两个特征将所研究的系统与理想模型区分开来。（仅限有限输入）已向系统输入，但可能无法随意设置整个内部状态。*（可变性）实验或模型运行是可重复的，但系统具有内部可变性，因此输出会受到随机性或干扰的影响。几个领域将作为更广泛的科学界的试验台和跳板：生态学、流行病学和社会科学中基于个人的模型，工程中的振动测试，气候子系统模型，和抽象空间扩展系统（例如用于神经元群体模型）。

The prediction and analysis of sudden changes in complex systems and models (called tipping) are a current topic in science and an urgent problem for society. A few hotly debated examples are the possible collapse of the Gulf Stream, the sudden loss of vegetation in nutrient-polluted lakes, or the change between the vegetated and desert state in dry regions. While these cases of tipping are well understood in idealised mathematical models, their analysis is restricted in field observations, laboratory experiments and complex model simulations by the impossibility to systematically explore dynamically unstable phenomena. For many complex systems the notion of equilibrium is only defined in a statistical mechanics sense as an emerging phenomenon, which, by its definition, must be stable.The proposed research will develop general mathematical methods that will remove these restrictions: they will enable experimenters and modellers to discover and track unstable phenomena in laboratory experiments and complex model simulations, or, more generally, in any situation where one can provide input into the system depending on its output in real time. Two features distinguish the systems under study from the idealised models.* (Limited input only) One has input into the system but may not be able to set the entire internal state at will.* (Variability) The experiment or model run is repeatable, but the system has internal variability such that outputs are affected by randomness or disturbances.Several areas will serve as testbeds and springboards to the wider scientific community: individual-based models in ecology, epidemiology and social science, vibration tests in engineering, models of climate subsystems, and abstract spatially extended systems (such as used for neuron population models).