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 throughan anticipatory mini-storage mechanism. In many real-world commodity markets, persistent price oscillations occur even whenclassical stability conditions are theoretically satisfied, an inconsistency traditional models fail to address. To bridge this gap, wedevelop 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 Aboodhtransform, enabling classification of market dynamics into underdamped, overdamped, and critically damped regimes. We eval-uate 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 pricevolatility and accelerates convergence to equilibrium. Sensitivity and phase-space analyses further demonstrate the model’s abilityto replicate diverse market behaviors, offering theoretical insights for policy interventions.