Linear stability analysis, attractors, limit cycles, Poincare-Bendixson
theorem, relaxation oscillations, elements of bifurcation theory:
saddle-node, transcritical, pitchfork, Hopf bifurcations,
integrability, Hamiltonian systems, Lotka-Volterra equations,
Lyapunov function & direct method for stability, dissipative systems,
Lorenz system, chaos & its measures, Lyapunov exponents, strange
attractors, simple maps, period-doubling bifurcations, Feigenbaum
Both flows (continuous time systems) & discrete time systems (simple
maps) will be discussed.
Assignments will include numerical simulations.
Prerequisites, if any: familiarity with linear algebra - matrices, and
ordinary differential equations
Desirable: ability to write codes for solving simple problems.
Suggested books and references:
S. Strogatz, Nonlinear Dynamics and Chaos: with Applications to physics, Biology, Chemistry, and Engineering, Westview, 1994.
S. Wiggins, Introduction to applied nonlinear dynamics & chaos, Springer-Verlag, 2003.
K. Alligood, T. Sauer, & James A.Yorke, Chaos: An Introduction to Dynamical Systems, Springer-Verlag, 1996.
M.Tabor, Chaos and Integrability in Non-linear Dynamics, 1989.