Size Of Stability Region Research Articles

Dynamic outcome of coopetition duopoly with implicit collusion

This paper mainly explores the influence of implicit collusion on the dynamic outcome of enterprises in coopetitive duopoly market. We construct a coopetitive duopoly model with implicit collusion, in which the narrowing price difference could be regarded as implicit collusion to drive the price up and avoid the risk of price wars brought by cutthroat competition. The dynamic coopetition duopoly model demonstrates the effect of implicit collusion on interior stable point. The equilibrium price of coopetitive balance with implicit collusion is higher than the Bertrand equilibrium price since implicit collusion maintains the prices at a high level. Furthermore, our model reveals that implicit collusion could bring back the enterprise, which has been dislodged from duopoly market on boundary stable point under certain parameter conditions. Besides, numerical simulations show a series of chaotic behaviors and present that the size of stability region is related to the values of parameters.

Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization

A dynamic Cournot duopoly model with isoelastic demand function and knowledge spillover effects is established, in which the goals of two enterprises are relative profit maximization. Since these two enterprises only have incomplete information of the market, then it is assumed that the enterprises are boundedly rational, and they need to adjust their production decision in next period according to the gradient adjustment mechanism. Sufficient conditions for the existence and stable properties of unique Nash equilibrium can be judged with the help of the Jury criterion. The size of stability region is related to the values of parameters and the system has two different paths to chaos, one is via flip bifurcation and another is via Neimark-Sacker bifurcation. Finally, the complex dynamic characteristics also can be further studied by using numerical simulation, including the structures of multi-layer Arnold's tongues and coexistence of attractors.

On the Stability ofL4,5in the Relativistic R3BP with Oblate Secondary and Radiating Primary

We consider a version of the relativistic restricted three-body problem (R3BP) which includes the effects of oblateness of the secondary and radiation of the primary. We determine the positions and analyze the stability of the triangular points. We find that these positions are affected by relativistic, oblateness, and radiation factors. It is also seen that both oblateness of the secondary and radiation of the primary reduce the size of stability region. Further, a numerical exploration computing the positions of the triangular points and the critical mass ratio of some binaries systems consisting of the Sun and its planets is given in the tables.

Moving Bragg grating solitons in a cubic-quintic nonlinear medium with dispersive reflectivity

The stability and collision dynamics of moving solitons in Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity are investigated. Two disjoint families of solitons are found on the plane of the coefficient of quintic nonlinearity versus the normalized frequency (η,Ω(norm)). Through numerical stability analysis, we have identified stability regions on the (η,Ω(norm)) plane for various values of dispersive reflectivity parameter (m) and velocity (v). The size of stability regions is found to be dependent on m and v. Collisions of counterpropgating Type 1 and Type 2 solitons have been systematically investigated. It is found that for low to moderate values of dispersive reflectivity, the collisions of Type 1 solitons can result in various outcomes such as separation of solitons with reduced, increased, unchanged, or asymmetric velocities and generation of a quiescent soliton by merger or formation of three solitons. For strong dispersive reflectivity (e.g., m=0.5), the collisions of low-velocity in-phase Type 1 solitons may lead to repulsion of solitons, asymmetric separation, merger into a single soliton, or formation of three solitons (one quiescent and two moving solitons). At higher velocities collisions predominantly lead to the formation of three solitons. For m=0.5, in-phase Type 2 solitons may repel or form a temporary bound state of quiescent Type 1 solitons that subsequently splits into two asymmetrically separating Type 1 solitons. π-out-of-phase Type 2 solitons may also merge to form a quiescent Type 1 soliton.

A Simple Mechanism that Causes Collapsing Stability Regions in Exploited Salmonid Populations

Depensatory predation mortality on salmon when added to a Ricker production model can create a system with at least two stable equilibria and two domains of attraction. The behavior of such a fish system is different from a single equilibrium situation and a simple mechanism is described through which commercial exploitation changes the ability of such multiple-equilibrium fish populations to respond to perturbations in survival rates. Furthermore, it is shown that this change in size of stability regions is proportional to the exploitation rate and that classically defined maximum sustainable yield (MSY) exploitation rates are inevitably close to the rates that would cause a drastic decrease in the population. The uncertainties inherent in environmental effects on survival and in achievement of desired exploitation rates precipitate the need to back away from the usual MSY exploitation rates and set up (through enhancement) a system of stocks whereby feedback information is provided to the manager. This approach of adaptive management seeks reasonable yields while gaining information about the state (or changes in state) of the system. Some applications of catastrophe theory are discussed, especially with reference to harvesting multiple-stock salmon systems. Key words: stability, resilience, exploitation, salmon, depensation, multiple equilibria, adaptive management, enhancement, catastrophe theory