Attractor and Lyapunov stability

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Difference between Attractor and Lyapunov stability

Attractor vs. Lyapunov stability

In the mathematical field of dynamical systems, an attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system. Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems.

Asymptotic analysis

In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.

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Chaos theory

Chaos theory is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions.

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Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

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Discrete time and continuous time

In mathematics and in particular mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.

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Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.

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Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.

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Linear system

A linear system is a mathematical model of a system based on the use of a linear operator.

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Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

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Nonlinear system

In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.

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Recurrence relation

In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.

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Stability theory

In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions.

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Stable manifold

In mathematics, and in particular the study of dynamical systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the idea of an attractor or repellor.

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Structural stability

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).

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Van der Pol oscillator

In dynamics, the Van der Pol oscillator is a non-conservative oscillator with non-linear damping.

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