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Near an unstable equilibrium, any system will be sensitive to noise, initial conditions and system parameters, which can cause it to develop in one of multiple divergent directions. In economics and social sciences, path dependence gives rise to divergent directions of development.
A ball located at this point, ball 3, is in equilibrium but unstable; the slightest disturbance will cause it to move to one of the stable points. Light switch, a bistable mechanism. In a dynamical system, bistability means the system has two stable equilibrium states. [1] A bistable structure can be resting in either of two states.
When is positive, there are two equilibrium points: that is, one saddle point and one node (either an attractor or a repellor). Other examples are in modelling biological switches. [ 4 ] Recently, it was shown that under certain conditions, the Einstein field equations of General Relativity have the same form as a fold bifurcation. [ 5 ]
The simplest kind of an orbit is a fixed point, or an equilibrium. If a mechanical system is in a stable equilibrium state then a small push will result in a localized motion, for example, small oscillations as in the case of a pendulum. In a system with damping, a stable equilibrium state is moreover asymptotically stable. On the other hand ...
A system in equilibrium in which there is positive feedback to any change from its current state may be unstable, in which case the system is said to be in an unstable equilibrium. The magnitude of the forces that act to move such a system away from its equilibrium is an increasing function of the distance of the state from the equilibrium.
At equilibrium, the center of mass and the contact point are on the line perpendicular to the ground. When the toy is pushed, its center of mass rises and shifts away from that line. This produces a righting moment, which returns the toy to its equilibrium position. The above examples of mono-monostatic objects are inhomogeneous.
Self-esteem stability refers to immediate feelings of self-esteem which, generally, will not be influenced by everyday positive or negative experiences. [1] In contrast, unstable self-esteem refers to fragile and vulnerable feelings of self-esteem which will be influenced by internally generated, such as reflecting on one's social life, and externally received evaluative information, for ...
An equilibrium point is hyperbolic if none of the eigenvalues have zero real part. If all eigenvalues have negative real parts, the point is stable. If at least one has a positive real part, the point is unstable.