This paper develops an Integrated Household Systems Framework (IHSF) that reconceptualizes poverty as a nonlinear dynamic equilibrium arising from interactions among cognitive, social, economic, and institutional processes. Unlike conventional approaches that treat constraints in isolation, households are modeled as coupled, state-dependent systems in which these dimensions co-evolve through endogenous feedback. The framework generates multiple equilibria and threshold dynamics, with poverty emerging as a locally stable state. Simulation results illustrate a critical threshold, below which trajectories converge to persistent poverty, while above it, they transition to self-sustaining growth. Crucially, marginal interventions and incremental policies yield only temporary gains, whereas sufficiently large and coordinated interventions can shift long-run outcomes. By integrating cross-domain complementarities into a unified dynamic system, the framework explains the limited effectiveness of isolated interventions and provides a tractable basis for analyzing poverty persistence, regime shifts, and multidimensional policy design.