Stability of a Continuous Reaction-Diffusion Cournot-Kopel Duopoly Game Model

Abstract

In order to take into account the territory in which the outputs are in the market and the time-depending firms' strategies, the discrete Cournot duopoly game (with adaptive expectations, modeled by Kopel) is generalized through a non autonomous reaction-diffusion binary system of PDEs, with self and cross diffusion terms. Linear and nonlinear asymptotic L2-stability, via the Liapunov Direct Methot and a nonautonomous energy functional, are investigated

Instability of Vertical Constant Through Flows in Binary Mixtures in Porous Media with Large Pores

“…with ∇ ⋅ u 0 (x) = 0. In the sequel, as usually is done in convection problems in layers, we suppose that We recall that the solutions of (10)- (12) are ultimately bounded since there exist positive invariant and attractive sets (absorbing sets) in the phase space as stated in the following theorem.…”

“…The models describing the fluid motion in porous media are reaction-diffusion dynamical systems of P.D.Es, which, as it is well known, play an important role in the modeling and studying of many phenomena {see, for instance, [11,12] and references therein}. Several geophysical and technological applications involve nonisothermal flow of fluids through porous media called throughflow (i.e., there is flow across the porous medium and the basic flows nonquiescent) which affects the stability of the system significantly.…”

Neimark–Sacker bifurcation and the generate cases of Kopel oligopoly model with different adjustment speed

“…A revised Kopel oligopoly model with extrapolative foresight was constructed by Gao, Zhong and Mei [11], and Neimark-Sacker bifurcation analysis showed the complex dynamics and the transitions between different dynamical systems. See more research about Kopel oligopoly model in [3,5,10,30,31,35]. As presented above in the related research, dynamical system theory was introduced as an important tool to explore the dynamics in oligopoly theory.…”

On the non-linear stability of a continuous duopoly model with constant conjectural variation

“…Different expectations such as naive expectations, adaptive expectations and bounded rationality have been proposed. Generalizations have been made for the Cournot-Kopel duopoly model [24], [21], by introducing self and cross diffusion terms in the equations 1 , when the outputs are in the market in large territories. Given a model, economists need to make predictions on the asymptotic behavior of the system i.e.…”