Cournot-Bertrand Duopoly Model: Dynamic Analysis Based on a Computed Cost
In this paper, some mathematical properties and dynamic investigations of a Cournot–Bertrand duopoly game using a computed
nonlinear cost are studied. +e game is repeated and its evolution is presented by noninvertible map. +e fixed points for this map
are calculated and their stability conditions are discussed. One of those fixed points is Nash equilibrium, and the discussion shows
that it can be unstable through flip and Neimark–Sacker bifurcation. +e invariant manifold for the game’s map is analyzed.
Furthermore, the case when both competing firms are independent is investigated. Due to unsymmetrical structure of the game’s
map, global analysis gives rise to complicated basin of attraction for some attracting sets. +e topological structure for these basins
of attraction shows that escaping (infeasible) domain for some attracting sets becomes unconnected and the rise of holes is
obtained. +is confirms the existence of contact bifurcation.
The parameter identification problem of photovoltaic (PV) models is classified as a complex nonlinear
optimization problem that cannot be accurately solved by traditional techniques.…
In this paper, some mathematical properties and dynamic investigations of a Cournot–Bertrand duopoly game using a computed
nonlinear cost are studied. +e game is repeated and its evolution…
Incorporating energy storage systems (ESSs) can mitigate the intermittency of renewable energy sources. There
are a variety of ESSs for renewable energy with vastly different characteristics…