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  2. Chaos theory - Wikipedia

    en.wikipedia.org/wiki/Chaos_theory

    The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions. Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions.

  3. Control of chaos - Wikipedia

    en.wikipedia.org/wiki/Control_of_chaos

    In lab experiments that study chaos theory, approaches designed to control chaos are based on certain observed system behaviors. Any chaotic attractor contains an infinite number of unstable, periodic orbits. Chaotic dynamics, then, consists of a motion where the system state moves in the neighborhood of one of these orbits for a while, then ...

  4. Robert L. Devaney - Wikipedia

    en.wikipedia.org/wiki/Robert_L._Devaney

    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 ...

  5. Dynamical systems theory - Wikipedia

    en.wikipedia.org/wiki/Dynamical_systems_theory

    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 ...

  6. List of chaotic maps - Wikipedia

    en.wikipedia.org/wiki/List_of_chaotic_maps

    Burke-Shaw chaotic attractor [8] continuous: real: 3: 2: Chen chaotic attractor [9] continuous: real: 3: 3: Not topologically conjugate to the Lorenz attractor. Chen-Celikovsky system [10] continuous: real: 3 "Generalized Lorenz canonical form of chaotic systems" Chen-LU system [11] continuous: real: 3: 3: Interpolates between Lorenz-like and ...

  7. Quantum chaos - Wikipedia

    en.wikipedia.org/wiki/Quantum_chaos

    Quantum chaos is a branch of physics focused on how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship between quantum mechanics and classical chaos ?"

  8. Mitchell Feigenbaum - Wikipedia

    en.wikipedia.org/wiki/Mitchell_Feigenbaum

    Although a complete theory of turbulent fluids remains elusive, Feigenbaum's research paved the way for chaos theory, providing groundbreaking insight into the many dynamical systems in which scientists and mathematicians find chaotic maps.

  9. Chua's circuit - Wikipedia

    en.wikipedia.org/wiki/Chua's_circuit

    The easy experimental implementation of the circuit, combined with the existence of a simple and accurate theoretical model, makes Chua's circuit a useful system to study many fundamental and applied issues of chaos theory. Because of this, it has been object of much study and appears widely referenced in the literature.