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  2. Lorenz system - Wikipedia

    en.wikipedia.org/wiki/Lorenz_system

    In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system. The term " butterfly effect " in popular media may stem from the real-world implications of the Lorenz attractor, namely that tiny changes in initial conditions evolve to completely different trajectories .

  3. Portal:Systems science/Picture - Wikipedia

    en.wikipedia.org/wiki/Portal:Systems_science/Picture

    The Lorenz attractor is a 3-dimensional structure corresponding to the long-term behavior of a chaotic flow, noted for its butterfly shape. The map shows how the state of a dynamical system (the three variables of a three-dimensional system) evolves over time in a complex, non-repeating pattern.

  4. 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 ...

  5. Dynamical system - Wikipedia

    en.wikipedia.org/wiki/Dynamical_system

    The Lorenz attractor arises in the study of the Lorenz oscillator, a dynamical system.. 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.

  6. Malkus waterwheel - Wikipedia

    en.wikipedia.org/wiki/Malkus_waterwheel

    The system indeed appears to exhibit a great dependence on initial conditions, a defining property of chaotic systems; moreover, two attractors of the system are seen in both plots. The Malkus waterwheel , also referred to as the Lorenz waterwheel or chaotic waterwheel , [ 1 ] is a mechanical model that exhibits chaotic dynamics.

  7. Wikipedia:Featured picture candidates/Lorenz attractor ...

    en.wikipedia.org/.../Lorenz_attractor_projection

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  8. Bifurcation diagram - Wikipedia

    en.wikipedia.org/wiki/Bifurcation_diagram

    Symmetry breaking in pitchfork bifurcation as the parameter ε is varied. ε = 0 is the case of symmetric pitchfork bifurcation.. In a dynamical system such as ¨ + (;) + =, which is structurally stable when , if a bifurcation diagram is plotted, treating as the bifurcation parameter, but for different values of , the case = is the symmetric pitchfork bifurcation.

  9. Autonomous system (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Autonomous_system...

    This should not be surprising, considering that nonlinear autonomous systems in three dimensions can produce truly chaotic behavior such as the Lorenz attractor and the Rössler attractor. Likewise, general non-autonomous equations of second order are unsolvable explicitly, since these can also be chaotic, as in a periodically forced pendulum. [6]