### MA6050 Dynamical systems

#### Course Details

One -dimensional flows: fixed points and stability, linear stability analysis, Saddle- node bifurcation, Transcritical bifurcation, Pitchfork bifurcation, Flows on the circle

Two -dimensional flows: Linear systems, nonlinear autonomous systems, phase portraits, Fixed points and linearization, conservative systems, index theory, limit cycles, Poincare Bendixson theorem, Lienard systems, Saddle-node, Transcritical and Pitchfork bifurcations, Hopf bifurcation

Chaos

Discrete dynamical systems

#### Course References:

Books:

(1) Steven H Strogatz, Nonlinear dynamics and Chaos, Perseus books publishing, 1994

(2) James T Sandefur, Discrete dynamical systems Theory and applications, Clarendon press, 1990