Stable Equilibrium

	Stable Equilibrium Stable equilibrium can refer to: Homeostasis, a state of equilibrium used to describe organisms Mechanical equilibrium, a state in which all particles in a system are at rest, and total force on each particle is permanently zero Balance of nature, a theory in ecological science Stability theory, a theory in mathematics Mertens-stable equilibrium in game theory Stochastically stable equilibrium In game theory, a stochastically stable equilibrium is a solution concept, refinement of the evolutionarily stable state in evolutionary game theory, proposed by Dean Foster and Peyton Young. An evolutionary stable state S is also stochastically s ... in the game theory {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Homeostasis In biology, homeostasis (British English, British also homoeostasis) Help:IPA/English, (/hɒmɪə(ʊ)ˈsteɪsɪs/) is the state of steady internal, physics, physical, and chemistry, chemical conditions maintained by organism, living systems. This is the condition of optimal functioning for the organism and includes many variables, such as body temperature and fluid balance, being kept within certain pre-set limits (homeostatic range). Other variables include the pH of extracellular fluid, the concentrations of sodium, potassium and calcium ions, as well as that of the blood sugar level, and these need to be regulated despite changes in the environment, diet, or level of activity. Each of these variables is controlled by one or more regulators or homeostatic mechanisms, which together maintain life. Homeostasis is brought about by a natural resistance to change when already in the optimal conditions, and equilibrium is maintained by many regulatory mechanisms: it is thought to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Mechanical Equilibrium In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. In addition to defining mechanical equilibrium in terms of force, there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent. In terms of momentum, a system is in equilibrium if the momentum of its parts is all constant. In terms of velocity, the system is in equilibrium if velocity is constant. In a rotational mechanical equilibrium the angular momentum of the object is conserved and the net torque is zero. More generally in conservative systems, equilibrium is established at a point in configuration space where the gradient of the potential energy with respect to the generalized coordinates is zero. If a particle in equilibrium has zero velocity, that particle is in static equilibrium. S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Balance Of Nature The balance of nature, also known as ecological balance, is a theory that proposes that ecological systems are usually in a stable equilibrium or homeostasis, which is to say that a small change (the size of a particular population, for example) will be corrected by some negative feedback that will bring the parameter back to its original "point of balance" with the rest of the system. The balance is sometimes depicted as easily disturbed and delicate, while other times it is inversely portrayed as powerful enough to correct any imbalances by itself. The concept has been described as "normative", as well as teleological, as it makes a claim about how nature ''should'' be: nature is balanced because "it is ''supposed to be'' balanced". The theory has been employed to describe how populations depend on each other, for example in predator-prey systems, or relationships between herbivores and their food source. It is also sometimes applied to the relationship between the Earth's ecosy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Stability Theory In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance. In dynamical systems, an orbit is called ''Lyapunov stable'' if the forward orbit of any point is in a small enough neighborhood or it stays in a small (but perhaps, larger) neighborhood. Various criteria have been developed to prove stability or instability of an orbit. Under favorable circumstances, the question may be reduced to a well-studied problem involvi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mertens-stable Equilibrium In game theory, Mertens stability is a solution concept used to predict the outcome of a non-cooperative game. A tentative definition of stability was proposed by Elon Kohlberg and Jean-François Mertens for games with finite numbers of players and strategies. Later, Mertens proposed a stronger definition that was elaborated further by Srihari Govindan and Mertens. This solution concept is now called ''Mertens stability'', or just ''stability''. Like other refinements of Nash equilibrium used in game theory stability selects subsets of the set of Nash equilibria that have desirable properties. Stability invokes stronger criteria than other refinements, and thereby ensures that more desirable properties are satisfied. Desirable Properties of a Refinement Refinements have often been motivated by arguments for admissibility, backward induction, and forward induction. In a two-player game, an admissible decision rule for a player is one that does not use any strategy that is weakly d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]