Generalized Systemic Resilience in High-Intensity Conflicts: Nonlocal Stochastic PDE Approach and Bifurcation Analysis

Abstract

This repository contains the preprint and accompanying materials for the paper: "Generalized Systemic Resilience in High-Intensity Conflicts: Nonlocal Stochastic PDE Approach and Bifurcation Analysis". We introduce a General Theory of Systemic Resilience (GST) based on a system of nonlocal stochastic partial differential equations (SPDEs), modeling the interaction between system complexity, adaptive lag, and tail risk. The work provides:- a functional-analytic SPDE framework for systemic resilience,- spectral and bifurcation analysis identifying collapse thresholds,- a cost functional capturing adaptive saturation effects,- a reproducible toy model illustrating phase transitions and heavy-tailed risk behavior. Included materials:- LaTeX source of the paper,- Python/Julia scripts for numerical simulations,- generated figures used in the manuscript. All results are fully reproducible via the provided code.