Sentence examples for uniqueness of the equilibrium from inspiring English sources

The existence and uniqueness of the equilibrium solutions are investigated through an equivalent mathematical programming formulation.

Here, the existence and uniqueness of the equilibrium point needs not to be considered.

Existence and uniqueness of the equilibrium point under more general conditions are also established.

Given this setup, we then investigate the important issues of existence and uniqueness of the equilibrium for the dynamical system, and of local asymptotic stability.

Some structural properties of the resulting model that pertain to controller design, such as uniqueness of the equilibrium point, feedback linearizability and local stability are shown to hold under conditions having direct physical interpretation.

We allow the model to have nondifferentiable and unbounded signal function, and use linear matrix inequality (LMI) framework and Homeomorphism theorem to prove the existence and uniqueness of the equilibrium, and derive some new sufficient condition ensuring global exponential stability of the networks.

We provide additional results on the problems of uniqueness, efficiency of the equilibrium, and convergence of a best-response-based dynamics to the equilibrium.

The existence and uniqueness of the Nash equilibrium in the mentioned games are explored and a computationally tractable distributed algorithm is designed to determine the equilibrium.

In Section 4, a non-cooperative energy-efficient uplink power control game is formulated, the existence and the uniqueness of the Nash equilibrium are discussed, and a pricing mechanism is introduced to improve the efficiency of the Nash equilibrium.

The end users autonomously trades-off between their utility and spectrum cost through transmission power control — essentially forming a non-cooperative power control game for which we show the existence and uniqueness of the Nash equilibrium.

The following theorem shows the existence and uniqueness of the positive equilibrium point of system (2).