Cobweb model with two delays: Stability and bifurcation
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Keywords:
Cobweb model, Stability, Delay differential equations, Hopf bifurcationAbstract
In this work, we study the fluctuations in the prices of agricultural and energy products. These prices are characterized by seasonality, where demand and supply conditions alternate cyclically with a precise and known periodicity. We investigate the dynamics of a cobweb model, consisting of a one-dimensional differential equation with two-time delays, to understand the impact of demand
and supply parameters on this cyclical behavior. We start by studying the linear stability analysis to find sufficient conditions under which the positive equilibrium is locally asymptotically stable. After choosing the delays as bifurcation parameters, we prove the existence of a family of periodic solutions that bifurcate from this equilibrium. Finally, we discuss their economic rationale with the help of numerical simulations.
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