Complex dynamics analysis for a duopoly model of common fishery resource
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In this paper, we formulate a dynamical model of commercial exploitations of renewable resources by assuming that two agents behave adaptively, following a bounded rationality adjustment process based on a local estimate of the marginal profit. We study the existence and the stability of the positive equilibrium characterizing the sustainable use of the renewable resource. Then we investigate the local bifurcations of the system through numerical simulation. We discover when one player accelerates the adjustment speed in order to achieve initial advantage, it may cause complex phenomena like quasi-period and chaos. Finally, we investigate a degraded two-dimensional system by showing the influence of the adjustment speed of the harvesting quantity on the set of initial conditions which give non-negative trajectories (called a feasible set). We find that higher adjustment speed may easily exhaust the resources.
KeywordsDynamical model of fish stock Bounded rationality Stability of the positive equilibrium Neimak–Sacker bifurcation
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