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The exhaustive list of topics in Nonlinear Dynamical Systems in which we provide Help with Homework Assignment and Help with Project is as follows:

  • Scalar differential equations
  • Examples of population dynamics
  • Definition of equilibrium point.
  • Vector differential equations
  • Solution for the linear case.
  • Vector fields and phase portraits.
  • Planar case:
    • Classification of equilibrium points
    • Relation with eigenvalues and eigenvectors
    • Phase portraits and vector fields.
  • Oscillators:
    • Van der Pol oscillators
    • Necessary conditions for periodic orbits
    • Sufficient conditions for such orbits.
  • Conditions for existence and uniqueness of solutions
  • Proof using fixed point theorem
  • Examples of non-uniqueness and finite-escape time features.
  • Lyapunov stability definition and theorem/proof
  • Converse theorems
  • Linearization about an equilibrium point.
  • Nyquist criterion
  • Feedback interconnections
  • Absolute stability
  • Lp stability
  • Small-gain theorem
  • Passivity results.
  • Loop transformations
  • Circle/Popov criteria
  • Derivations.
  • Describing function method.