Attractor and Initial condition

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Difference between Attractor and Initial condition

Attractor vs. Initial condition

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. In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t.

Butterfly effect

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

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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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Coordinate vector

In linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers that describes the vector in terms of a particular ordered basis.

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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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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Matrix difference equation

A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices.

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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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