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Explore how snow, land use, and economic activity interact in the Aysén basin

This tool translates the mathematical equations behind the Computational Network Model into an interactive experience. Instead of running complex software, you can adjust key environmental and socio-economic parameters using the sliders on the left and instantly see how biomass, livestock, employment, and income respond over time. The underlying equations — the same ones validated in the D4.4 Annexes — are solved in real time, making it possible to explore "what-if" scenarios such as snow droughts or overgrazing directly from the platform.

Forage Biomass (x₁)

N(t)-modulated

Livestock Density (x₂)

Normalised

Employment (x₃)

Normalised

Net Income (x₄)

Normalised

Phase Portrait — All State Variables

t = 0 → 100 days
Biomass x₁ Livestock x₂ Employment x₃ Income x₄
solver: RK4 (h=0.1) steps: 10000 status: ready

Multi-Scale Hierarchical Architecture

Two-Layer Complex Network · Aysén Basin
MICRO
Pixel / Agent Scale — EO Data Ingestion
High-resolution Sentinel-2 imagery → Snow Persistence N(t) via NDSI + Random Forest binary classification. Multi-sensor LULC (Sentinel-1 SAR + Sentinel-2 optical + DEM topographic) → Patch land-use classification. Ingested via OGC WMS/WCS → PostgreSQL/PostGIS spatial database.
⇣ N(t), Lᵢ(t) forcing ⇣
MESO
Patch Scale — Functional Subsystems
Territory discretised into 9 patch types: Agricultural (A), Livestock (G), Forestry (F), Tourism-General (T), Tourism-Fishing (P), Rural (R), Urban (U), Salmon (S), Unused (Z). Each patch governed by 4-variable ODE system: xᵢ = [biomass, livestock, employment, income]. Snow forcing N(t) modulates logistic growth. Inter-patch coupling via mobility matrix wᵢⱼ.
⇣ Aggregated R(t) ⇣
MACRO
Basin Scale — Aggregated Dynamics
State vector: [L, N, F, H] = [Population, Non-renewable resources, Fisheries, Social index]. Renewable resources R = Σ(MESO patches) → bottom-up coupling. Captures slow structural constraints: demographic trends, resource depletion, social feedback loops.
Layer 1: Uncontrolled SLW System (Stochastic)
Snow-Land-Water environmental forcing. Meteorological drivers + Copernicus Sentinel-2 time series → continuous dimensionless forcing function N(t) that modulates vegetation growth rates and hydrological availability.
Layer 2: Controlled Land-Use System (Deterministic + SDE)
Socio-economic dynamics discretised into functional patches. Each node governed by ODEs with multiplicative noise terms (SDE extension) for climate uncertainty. Network edges represent mobility and economic flow matrices between nodes.
Source: Deliverable D4.4 — Annexe 1 & 2 · MatCont/MATLAB validation · COMUNIDAD Project (GA 101136910)

ODE System — Mathematical Formulation

Dimensionless form · MatCont validated

MESO Level — Agricultural-Livestock Patch (Ñirehuao)

dx₁/dt = (1 + α·N)·x₁·(1 − x₁) − β·x₁·x₂ − (δ₁ + δₜ)·x₁
dx₂/dt = γ·x₁·x₂ − δ₂·x₂ + π
dx₃/dt = η·x₂·(1 − x₃) − δ₃·x₃
dx₄/dt = ρ·x₂ − δ₄·x₄ − χ
Where: x₁ = normalised forage biomass, x₂ = livestock density, x₃ = employment rate, x₄ = net income. N(t) = snow persistence forcing from Sentinel-2. Parameters calibrated for Ñirehuao sector, Aysén.

MACRO Level — Basin Scale

dL/dt = γ·(P − σ)·L
dN/dt = −α_j·β_n·L
dF/dt = ρ·F·(1 − F/K_f) − α·β_f·L·F
dH/dt = q·G_e·(m₁R + m₂N)·H·(1−H)·(1−L/Lᵢ)·(L/Lₐ−1)·L
Where: L = total population, N = non-renewable resources, F = fisheries, H = social index. R = renewable resources (aggregated from MESO). Basin-wide slow dynamics providing structural constraints.

Network Coupling Structure

dxᵢ/dt = fᵢ(xᵢ, pᵢ, ηᵢ(t)) + Σⱼ wᵢⱼ·(xⱼ − xᵢ)
General inter-patch coupling: wᵢⱼ represents mobility and economic flow weights between patches. The directed network ensures information flows across scales: MICRO → MESO → MACRO.
COMUNIDAD Project · Horizon Europe · GA 101136910 · Connecting Europe and Latin America