Search results
Results From The WOW.Com Content Network
Other terms used include grave, extremely critical, critical but stable, serious but stable, guarded, [3] and satisfactory.. The American Hospital Association has advised doctors not to use the word "stable" either as a condition or in conjunction with another condition, especially one that is critical, as it inherently implies unpredictability and the instability of vital signs. [2]
Nonchaotic orbits eventually approach one of two stable critical points, as shown with large blue dots. Chaotic and nonchaotic orbits occupy different regions of attraction within the phase space. In contrast to single type chaotic solutions, recent studies using Lorenz models [ 41 ] [ 42 ] have emphasized the importance of considering various ...
To determine whether the flow is stable or unstable, one often employs the method of linear stability analysis. In this type of analysis, the governing equations and boundary conditions are linearized. This is based on the fact that the concept of 'stable' or 'unstable' is based on an infinitely small disturbance.
In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. One example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a liquid and its vapor can coexist.
In the former case, the orbit is called stable; in the latter case, it is called asymptotically stable and the given orbit is said to be attracting. An equilibrium solution f e {\displaystyle f_{e}} to an autonomous system of first order ordinary differential equations is called:
This is often observed in vibrating systems, such as a clock pendulum, but can happen with any type of stable or semi-stable dynamic system. The length of the transient state will depend on the initial conditions of the system. Given certain initial conditions, a system may be in steady state from the beginning.
Graphical representation of alternative stable states and the direction of critical slowing down prior to a critical transition (taken from Lever et al. 2020). [12] Top panels (a) indicate stability landscapes at different conditions.
In 1957 R. E. Kalman in his paper [1] stated the following: . If f(e) in Fig. 1 is replaced by constants K corresponding to all possible values of f'(e), and it is found that the closed-loop system is stable for all such K, then it intuitively clear that the system must be monostable; i.e., all transient solutions will converge to a unique, stable critical point.