Global dynamics in a commodity market model

Abstract

a b s t r a c tWe study the global behavior of the price dynamics in a commodity market governed by a balance between demand and supply. While the dependence of demand on price is considered instantaneous, the supply term contains a delay, leading to a delay-differential equation. A discrete model is naturally defined as a limit case of this equation. We provide a thorough study of the discrete case, and use these results to get new sufficient conditions for the global convergence of the solutions to the positive equilibrium in the continuous case. For when the equilibrium is unstable, we provide some bounds for the amplitude of the oscillations that are quite sharp when the delay is large.

Endemic Bubbles Generated by Delayed Behavioral Response: Global Stability and Bifurcation Switches in an SIS Model

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Delayed logistic population models revisited

“…Pioneering work is due to Mallet-Paret and Nussbaum [32,33], and Ivanov and Sharkovsky [23]. For recent results, see [29,30,31,45,55].…”

New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems

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