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This analogy with mechanical equilibrium motivates the terminology of stability and instability. In mathematics, and especially algebraic geometry, stability is a notion which characterises when a geometric object, for example a point, an algebraic variety, a vector bundle, or a sheaf, has some desirable properties for the purpose of ...
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 mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of the trajectories is unaffected by small perturbations (to be exact C 1-small perturbations). Examples of such qualitative properties are numbers of fixed points and periodic orbits (but not their periods).
In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the form / =, where r is the perturbation to the steady state, A is a linear operator whose spectrum contains eigenvalues with positive real part.
[3] When the CoG moves beyond the BoS, the individual must take a step or hold onto an external support to maintain balance and prevent a fall. [4] [5] These stability limits are perceived rather than solely physiological; they represent the subject's readiness to adjust their CoG position. [1]: 25
Within mathematics regarding differential equations, L-stability is a special case of A-stability, a property of Runge–Kutta methods for solving ordinary differential equations.
Stability generally increases to the left of the diagram. [1] Some sink, source or node are equilibrium points. 2-dimensional case refers to Phase plane. In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable.
A group of finite Morley rank is an abstract group G such that the formula x = x has finite Morley rank for the model G.It follows from the definition that the theory of a group of finite Morley rank is ω-stable; therefore groups of finite Morley rank are stable groups.