Most of atoms and molecule found in nature are capable of evolving towards and staying at their ground states, the lowest energy states. This paper offers a global optimization approach to understand the ground state as the equilibrium point of an n-player game under cooperation. With the same approach, Nash equilibrium can be viewed as the equilibrium point under competition. The former can of...

Abstract. In this paper the stability of equilibrium points of the nonlinear differential equation with fractional nonlinearity is studied. It is supposed that this system is exposed to additive stochastic perturbations that are of the type of white noise and are directly proportional to the deviation of the system state from the equilibrium point. Sufficient conditions for stability in probabi...

It is a well known fact that the local stability of an equilibrium point in a system of ordinary differential equations doesnot necessarily imply its global stability. However, the usual methods used in the analysis of stability of equilibrium points in population models establishes only local stability. The restriction to sufficiently small perturbations of the initial conditions frequently ru...

This paper discusses an optimization-based technique for determining the stability of a given equilibrium point of the unilaterally constrained structural system, which is subjected to the static load. We deal with the three problems in mechanics sharing the common mathematical properties: (i) structures containing no-compression cables; (ii) frictionless contacts; (iii) elastic-plastic trusses...

The network equations of electric power system are formed in which the node voltages and branch currents are as state variables by π equivalent circuit simulation of power components. The explicit expressions of power system voltage equilibrium solution curves are obtained by solving the equations above, and then get the characteristic equation of the saddle-node bifurcation point, define the f...

This paper discusses an optimization-based technique for determining the stability of a given equilibrium point of the unilaterally constrained structural system, which is subjected to the static load. We deal with the three problems in mechanics sharing the common mathematical properties: (i) structures containing nocompression cables; (ii) frictionless contacts; and (iii) elastic–plastic trus...

In this paper, the authors are concerned with the stability of the mix–delayed CohenGrossberg neural networks with nonlinear impulse by the nonsmooth analysis. Some novel sufficient conditions are obtained for the existence and the globally asymptotic stability of the unique equilibrium point, which include the well-known results on some impulsive systems and non-impulsive systems as its partic...

In this paper, an SIR epidemic model with nonlinear incidence rate and double delays due to the force of infection and temporary immunity period is investigated. The existence and stability of the possible equilibria are examined in terms of a certain threshold condition R0, the basic reproduction number. Based on some comparison arguments, sharp threshold conditions which are necessary for the...

We extend previous work that analyzes the stability of evolutionary dynamics on probability distributions over continuous strategy spaces. The stability concept considered is that of bneighborhoodQ convergence to a rest point (i.e. an equilibrium distribution over the strategy space) under the dynamics in the weak topology for all initial distributions whose support is close to that of the rest...

We consider resource allocation games with heterogeneous users and identical resources. Most of the previous work considered cost structures with either negative or positive congestion effects. We study a cost structure that encompasses both the resource’s load and the job’s share in the resource’s activation cost. We consider the proportional sharing rule, where the resource’s activation cost ...