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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 ...
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time , this means that for those properties p of the system, the partial derivative with respect to time is zero and remains so:
The mathematical theory of stability of motion, founded by A. M. Lyapunov, considerably anticipated the time for its implementation in science and technology. Moreover Lyapunov did not himself make application in this field, his own interest being in the stability of rotating fluid masses with astronomical application.
Spirule. In control theory and stability theory, root locus analysis is a graphical method for examining how the roots of a system change with variation of a certain system parameter, commonly a gain within a feedback system.
Hegemonic stability theory (HST) is a theory of international relations, rooted in research from the fields of political science, economics, and history. HST indicates that the international system is more likely to remain stable when a single state is the dominant world power, or hegemon . [ 1 ]
The Nyquist plot for () = + + with s = jω.. In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker [] at Siemens in 1930 [1] [2] [3] and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, [4] is a graphical technique ...
Stability–change is "a class of relational dialectics that includes certainty–uncertainty, conventionally–uniqueness, predictability–surprise, and routine–novelty." [11] Things must be consistent but not mundane. There must be a balance between the expected and unexpected in order to keep a relationship.
Social exchange theory is a sociological and psychological theory that studies the social behavior in the interaction of two parties that implement a cost-benefit analysis to determine risks and benefits. The theory also involves economic relationships—the cost-benefit analysis occurs when each party has goods that the other parties value. [1]