MA416: Nonlinear Dynamical Systems

Realistic models of the physical world are nonlinear, involving large amplitudes of motion and thus usually several equilibria of the system concerned. This course gives the background for the analysis and synthesis (design) of dynamic behaviour of general networks, which represent a large class of nonlinear systems, predominantly physical and in particular mechanical. Research projects will involve the application of nonlinear techniques to analyse the properties of nonlinear systems. It is essential that the

student is well-versed in one of the computing languages or computer algebra systems such as Mathematica.

 

The major topics that we will be covered are the following:

·         Systems of First-Order Linear Equations: systems of linear algebraic equations; linear independence; eignevalues; eigenvectors; homogeneous linear systems with constant coefficients; complex eigenvalues; repeated eignenvalues;

·         Nonlinear Differential Equations and Stability; the phase plane; autonomous systems and stability; almost linear systems; Lyapunov’s Second Method; periodic solutions and limit cycles; chaos and strange attractors.