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The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice—once for differential equations and once again for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale (also known as a time-set ...
Phase portrait showing saddle-node bifurcation. Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations.
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum , the flow of water in a pipe , the random motion of particles in the air , and the number of fish ...
Claude Shannon used symbolic sequences and shifts of finite type in his 1948 paper A mathematical theory of communication that gave birth to information theory. During the late 1960s the method of symbolic dynamics was developed to hyperbolic toral automorphisms by Roy Adler and Benjamin Weiss , [ 3 ] and to Anosov diffeomorphisms by Yakov ...
Catastrophe theory studies dynamical systems that describe the evolution [5] of a state variable over time : ˙ = = (,) In the above equation, is referred to as the potential function, and is often a vector or a scalar which parameterise the potential function.
This is a list of scientific journals covering mathematics with existing Wikipedia articles on them. Alphabetic list of titles. A. Abhandlungen aus dem Mathematischen ...
Dynamic programming is both a mathematical optimization method and an algorithmic paradigm. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics .
Devaney is known for formulating a simple and widely used definition of chaotic systems, one that does not need advanced concepts such as measure theory. [8] In his 1989 book An Introduction to Chaotic Dynamical Systems, Devaney defined a system to be chaotic if it has sensitive dependence on initial conditions, it is topologically transitive (for any two open sets, some points from one set ...
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