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Watershed Algal Dynamics: Uncertainty Quantification and Sensitivity Analysis in Reaction–Diffusion Models |
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PP: 891-907 |
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doi:10.18576/jsap/140626
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Author(s) |
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Yogeesh N.,
Suleiman Ibrahim Al-Hawary,
Shankaralingappa B. M.,
Asokan Vasudevan,
Dinesh V.,
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Abstract |
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| This chapter develops a math-to-policy pipeline for coupled environmental and social systems. We formalize states
of nature 𝑥(𝑡) and society 𝑦(𝑡) as interacting dynamical systems, moving from deterministic ODEs to reaction-diffusion
PDEs, network dynamics, agent-based models, and state-space formulations. Core analyses include equilibria, local stability
(Jacobian spectra), thresholds (basic reproduction/contagion ratios and spectral radii), traveling-wave speeds for spatial
spread, and optimalcontrol formulations with quadratic penalties. Uncertainty is treated via stochastic differential equations,
Monte Carlo, spectral (polynomial-chaos) surrogates, and global variance-based sensitivity (Sobol indices). Two detailed
case studies demonstrate end-to-end use: (A) a watershed nutrient-algae model identifies a feasible stable equilibrium,
management thresholds to cap biomass, and a reaction-diffusion wave-speed rule 𝑐!"# = 2√𝐷𝑟 for containment; (B) a social
technology-adoption model yields a crisp policy threshold 𝑢 = 𝑟 /𝜂 for eliminating an undesirable incumbent, closed- min $
form time courses under constant control, and a network refinement linking required effort to the spectral radius of the contact graph. Calibration sketches, elasticity insights, and screening rules translate the mathematics into actionable guidance (front- loaded controls; targeted interventions that reduce spectral connectivity). The chapter concludes with limitations (structure, identifiability, data scale) and future directions (stochastic control, equity-aware objectives, real-time assimilation). Overall,
the chapter shows how transparent mathematical structures produce quantitative levers for sustainability decisions
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