Jesús Paz · Research

Dynamical systems · memory · structures · information

Research on dynamical systems, structures, information, and the organizational processes of nature. Development of theory, models, and tools with mathematical rigor and computational validation.

TheoryModelsComputational validation

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Structural Prevalence Theory

A developing research framework on dynamics, history, and structure.

Evolution is studied through path dependence, attractors, separatrices, and the structural conditions that favor the persistence of particular regimes.

Explore TSP →Publication on Zenodo ↗

\frac{d u}{d τ} = u - \hat{χ} u^{2} + \hat{κ} u^{2 + δ}

Conceptual diagram; it does not represent a quantitative result.

A concrete case

A concrete case: the canonical model

With χ̂ = 2.5, κ̂ = 1.0, δ = 1.0, the equation factors as du/dτ = u(u − 0.5)(u − 2).

u*₀ = 0 — unstable
u*₁ = 0.5 — stable; homeostasis regime
u*₂ = 2.0 — unstable; acts as separatrix

Any initial condition below u*₂ converges to homeostasis; above it, the system enters the prevalence regime. It’s a minimal case, but fully verifiable — which is why it’s the most honest starting point for evaluating the proposal.

See the full formulation →

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