Interdisciplinary Study on Reconstruction of Oligopoly and Duopoly theory based on Nonlinear Dynamic theory

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This study extends the traditional dynamics study on Oligopoly and Duopoly models in two directions : one is to consider the effects caused by strong nonlinearities on dynamics, using the nonlinear economic dynamics theory and the other is to consider the effect caused by spatial factors.The main results that we obtain are the followings.1.Construction of attractor sets that trajectories converge when a stationary point is locally unstable.2.Clarification of the relation between parameters values and the structure of basin in a case of multistability.3.Construction of analytical solutions when a stationary state is locally stable.4.Possible occurrence of complex dynamics when spatial elements are introduced into the traditional regional model.5.Comparison of the effect caused by a delayed stabilization policy with the effect caused by spatial elements.