We construct a generic ecosystem model that features the basic mechanisms of alternative stable states as well as two different stochastic influences. In particular, we use a mean-reverting jump-diffusion process to model the evolution of the ecosystem state over time. We review key concepts of multistability theory and the simple heuristics commonly employed to illustrate them. We then provide mathematical definitions for these concepts in the model context. Our contribution to the literature is twofold: we improve the representation of stochasticity in, and clarify key concepts of, multistability theory. The simplicity of the model enables a number of applications, such as finding economically optimal management strategies, identifying criteria for sustainable ecosystem management in a stochastic viability framework, deriving the probability of a regime shift, or empirically identifying the factors which have caused a specific regime shift.

中文翻译：

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具有替代稳定状态的随机生态系统的程式化模型

我们构建了一个通用生态系统模型，该模型具有替代稳定状态的基本机制以及两种不同的随机影响。特别是，我们使用均值回复跳跃扩散过程来模拟生态系统状态随时间的演变。我们回顾了多稳定性理论的关键概念以及通常用来说明它们的简单启发式方法。然后，我们在模型上下文中为这些概念提供数学定义。我们对文献的贡献是双重的：我们改进了随机性的表示，并阐明了多稳定性理论的关键概念。该模型的简单性使许多应用成为可能，例如寻找经济上最优的管理策略，在随机可行性框架中确定可持续生态系统管理的标准，