Dynamic behavior in a Cournot duopoly with social responsibility

In an oligopoly with isoelastic demand, the paper analyzes the quantity competition between NPM profit-maximizing firms and NRS socially responsible firms whose objective function is a linear combination of profit and consumer surplus. From the static analysis it follows that greater social responsibility has a competitive effect, since reduces the equilibrium price and increases the market share of socially responsible firms. In addition, it increases both the consumer surplus and total surplus. For the duopoly case, the dynamic study leads to the conclusion that, if at least one of the firms follows the gradient rule as an adjustment mechanism, an increase in the speed of adjustment is a source of instability. An increase in the value of the elasticity of demand as well as a reduction in the marginal cost has a stabilizing effect on the Cournot equilibrium. A higher level of social responsibility exerts a stabilizing role on the dynamics as long as demand is sufficiently elastic

Nonlinear Cournot and Bertrand-type dynamic triopoly with differentiated products and heterogeneous expectations

In a differentiated triopoly model with heterogeneous firms, the local stability of the Nash equilibrium under both quantity and price competition is analyzed. We find that the presence of a firm following a gradient rule based on marginal profits, and a player with adaptive expectations, determines the local stability of the Nash equilibrium, regardless the competition type, while the effects of the degree of product differentiation on the stability depend on the nature of products. Moreover, the Nash equilibrium is more stable under quantity competition than under price competition

Dynamics of solitary waves, chaotic behaviors, and Jacobi elliptic wave solutions in telecommunication systems

This research explores bifurcation of a nonlinear model concerning with the telecommunication strait. Possible all phase plane diagrams due to various parametric conditions are found. Derivation of analytical tangled wave propagating solutions following all phase orbits of the corresponding phase portraits are established. As a results, the soliton, shock wave, singular soliton, periodic wave and singular periodic solutions are obtained by direct integration from Hamiltonian energy function. The periodic solutions of the model are formulated in the form of generalized Jacobi elliptic functions, which also provide the solitonic solution setting the value of beta is unity. Additionally, chaotic and quasi-periodic behaviors have been found for a range of parameter values after adding the perturbed term. The perturbed system’s quasi-periodic and chaotic behavior have been demonstrated using sensitivity analysis. Finally, picturesque explorations are delivered exposing effects of exist parameters of the gained wave solutions. The majority of the achieved results are derived for the first time. Moreover, the solutions show that the novel schemes are very simple, outright, fruitful and successful and that they can be used in wide range of other nonlinear partial differential equations (NLPDEs), which create different kinds of dynamical features of other wave model