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.