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Download as PDF; Printable version; In other projects ... L-stability is a special ... is the stability function of the method (the stability function of a Runge ...
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.
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 ...
Comparison functions are primarily used to obtain quantitative restatements of stability properties as Lyapunov stability, uniform asymptotic stability, etc. These restatements are often more useful than the qualitative definitions of stability properties given in ε - δ {\displaystyle \varepsilon {\text{-}}\delta } language.
A Lyapunov function for an autonomous dynamical system {: ˙ = ()with an equilibrium point at = is a scalar function: that is continuous, has continuous first derivatives, is strictly positive for , and for which the time derivative ˙ = is non positive (these conditions are required on some region containing the origin).
An L-series is a Dirichlet series, usually convergent on a half-plane, that may give rise to an L-function via analytic continuation. The Riemann zeta function is an example of an L -function, and some important conjectures involving L -functions are the Riemann hypothesis and its generalizations .
In mathematics, the master stability function is a tool used to analyze the stability of the synchronous state in a dynamical system consisting of many identical systems which are coupled together, such as the Kuramoto model. The setting is as follows. Consider a system with identical oscillators.
A cobweb plot, known also as Lémeray Diagram or Verhulst diagram is a visual tool used in the dynamical systems field of mathematics to investigate the qualitative behaviour of one-dimensional iterated functions, such as the logistic map.