Dynamical Systems

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About Course

Dynamical Systems (DS).

n mathematics, a Dynamical Systems is a system in which a function describes the time dependence of a point in a geometrical space.

Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.

At any given time, a dynamical system has a state given by a tuple of real numbers (a vector) that can be represented by a point inappropriate state space (a geometrical manifold). The evolution rule of the dynamical system is a function that describes what future states follow from the current state. Often the function is deterministic, that is, for a given time interval only one future state follows from the current state. However, some systems are stochastic, in that random events also affect the evolution of the state variables.

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What Will You Learn?

  • Learn the basics of Dynamical Systems

Course Content

Dynamical Systems

  • Sparse Identification of Nonlinear Dynamics (SINDy)
    00:00
  • Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control
    00:00
  • Koopman Observable Subspaces & Nonlinearization
    00:00
  • Koopman Operator Optimal Control
    00:00
  • Compressed Sensing and Dynamic Mode Decomposition
    00:00
  • Hankel Alternative View of Koopman (HAVOK) Analysis [FULL]
    00:00
  • Hankel Alternative View of Koopman (HAVOK) Analysis [SHORT]
    00:00
  • Magnetic field reversal and Measles outbreaks: HAVOK models of chaos
    00:00
  • Linear model for chaotic Lorenz system [HAVOK]
    00:00
  • Simulating the Lorenz System in Matlab
    00:00
  • Discrete-Time Dynamical Systems
    00:00
  • Simulating the Logistic Map in Matlab
    00:00
  • Deep Learning of Dynamics and Coordinates with SINDy Autoencoders
    00:00

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