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Autonomous Equation
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. When the variable is time, they are also called time-invariant systems. Many laws in physics, where the independent variable is usually assumed to be time, are expressed as autonomous systems because it is assumed the laws of nature which hold now are identical to those for any point in the past or future. Definition An autonomous system is a system of ordinary differential equations of the form \fracx(t)=f(x(t)) where takes values in -dimensional Euclidean space; is often interpreted as time. It is distinguished from systems of differential equations of the form \fracx(t)=g(x(t),t) in which the law governing the evolution of the system does not depend solely on the system's current state but also the parameter , again often interpreted as time; such systems are by definition not autonomous. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stability Diagram
Stability may refer to: Mathematics *Stability theory, the study of the stability of solutions to differential equations and dynamical systems **Asymptotic stability **Linear stability **Lyapunov stability **Orbital stability **Structural stability *Stability (probability), a property of probability distributions *Stability (learning theory), a property of machine learning algorithms *Stability, a property of sorting algorithms *Numerical stability, a property of numerical algorithms which describes how errors in the input data propagate through the algorithm *Stability radius, a property of continuous polynomial functions *Stable theory, concerned with the notion of stability in model theory *Stability, a property of points in geometric invariant theory *K-Stability, a stability condition for algebraic varieties. *Bridgeland stability conditions, a class of stability conditions on elements of a triangulated category. *Stability (algebraic geometry) Engineering *In atmospheric flui ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
