Bifurcation and stability analysis of a cross‐diffusion vegetation‐water model with mixed delays

Xiong, Zixiao; Zhang, Qimin; Kang, Ting

doi:10.1002/mma.7384

Cited by 7 publications

(1 citation statement)

References 21 publications

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“…Phillips (1990, 1991) updated that analysis, defining interactions based on flow resistance equations. Other examples of Routh–Hurwitz stability analyses in hydrology, aquatic ecology and fluid mechanics include Phillips and Steila (1984), Phillips (2017), Wengert et al (1999), Dambacher et al (2009), Redondo et al (2020), Ahuja and Girotra (2021), Xiong et al (2021) and Hai and Daripa (2022).…”

Section: Methodsmentioning

confidence: 99%

Contingent partitioning and adaptation in hydrological systems

Phillips

2023

Ecohydrology

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The question of whether the concept of adaptation can be applied to Earth surface systems (independently of biological adaptation) is addressed by examining hydrological flow systems. Hydrological systems are represented in terms of a partitioning of water inputs among various flux and storage components and outflows or outputs of the system. Partitioning is contingent on the flow system in question and the synoptic situation (i.e., drier, low‐input vs. wetter, high‐input conditions). The general allocation among inputs, flows through or within the system, storage and outputs is examined via analysis of 20 scenarios for soil hydrology, a fluvial channel‐wetland complex and a fluviokarst landscape representing different combinations of positive, negative and zero (neutral) relationships among these elements, and positive self‐reinforcing and negative self‐limiting effects. Conditions for stability were determined using the Routh–Hurwitz criteria and linked to the two fundamental roles or ‘jobs’ of hydrological flow systems. The ecological job is to support biota and biogeochemical fluxes and transformations necessary for ecosystem functions. The geophysical job is to remove excess water. Results show that low‐input scenarios for the soil, fluvial wetland and fluviokarst scenarios are marked by dynamical instability. During drier periods the geophysical job is irrelevant and the ecological functions are suboptimal. Instability allows for rapid state changes when moisture inputs increase, to system states that support ecosystem functions. High‐input, excess moisture and flood scenarios, by contrast, are generally dynamically stable. In wetter conditions, the ecological functions are not moisture‐stressed, and the geophysical job becomes paramount. The high‐input stability is associated with activation of ‘spillway’ mechanisms that allow the systems to maintain themselves by efficient export and augmented storage of excess water. Contingent partitioning indeed appears to be an adaptation mechanism in hydrological systems and suggests the possibility of adaptation in other Earth surface systems with important abiotic components.

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