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The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calculations practical, while figures and images made it possible to ...
Experimental control of chaos by one or both of these methods has been achieved in a variety of systems, including turbulent fluids, oscillating chemical reactions, magneto-mechanical oscillators and cardiac tissues. [6] attempt the control of chaotic bubbling with the OGY method and using electrostatic potential as the primary control variable.
More precisely, this example works to explain a kind of math called chaos theory, which looks at how small changes made to a system’s initial conditions—like the extra gust of wind from a ...
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems.Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does ...
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 ...
Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; Asymptotic theory; Automata theory; Bass–Serre theory; Bifurcation theory; Braid theory
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.
Some mathematical mappings involving a single linear parameter exhibit the apparently random behavior known as chaos when the parameter lies within certain ranges. As the parameter is increased towards this region, the mapping undergoes bifurcations at precise values of the parameter. At first, one stable point occurs, then bifurcates to an ...