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This paper analyzed the dynamics of Cournot duopoly game with a logarithmic demand function. We assumed that the owners of both firms played with bounded rationality expectation. The existence of equilibrium points and its local stability of the output game are investigated. The complex dynamics, bifurcations and chaos are displayed by numerical experiments. Numerical methods showed that the higher values of speeds of adjustment act on the Nash equilibrium that becomes unstable through period doubling bifurcations, more complex attractors are created around it. The chaotic behavior of the game has been controlled by using feedback control method. we investigated the mechanisms that lead the firms to behave in the same way in the long run (synchronization phenomena).

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