Behavioral Cobweb Dynamics With Anticipatory Inventory and Ulam Stability: An Integro‐Differential Approach

This paper proposes a novel extension of the classical cobweb price model by incorporating behavioral inventory responses through an anticipatory mini-storage mechanism. In many real-world commodity markets, persistent price oscillations occur even when classical stability conditions are theoretically satisfied, an inconsistency traditional models fail to address. To bridge this gap, we develop an integro-differential model that captures both immediate supply–demand imbalances and cumulative memory effects, reflecting how suppliers adjust inventory in response to expected price shifts. Analytical solutions are derived using the Aboodh transform, enabling classification of market dynamics into underdamped, overdamped, and critically damped regimes. We evaluate the system's robustness under bounded perturbations using Hyers–Ulam and Hyers–Ulam–Rassias stability frameworks, confirming its structural stability. Numerical simulations show that incorporating anticipatory storage significantly dampens price volatility and accelerates convergence to equilibrium. Sensitivity and phase-space analyses further demonstrate the model's ability to replicate diverse market behaviors, offering theoretical insights for policy interventions.