MA 278: Introduction to Dynamical Systems Theory

Credits: 3:0

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 constants, fractals. 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:

  1. S. Strogatz, Nonlinear Dynamics and Chaos: with Applications to physics, Biology, Chemistry, and Engineering ,Westview, 1994.
  2. S. Wiggins, Introduction to applied nonlinear dynamics & chaos ,Springer-Verlag, 2003.
  3. K. Alligood, T. Sauer, & James A.Yorke, Chaos: An Introduction to Dynamical Systems ,Springer-Verlag, 1996.
  4. M.Tabor, Chaos and Integrability in Non-linear Dynamics ,1989.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265
E-mail: chairman.math[at]iisc[dot]ac[dot]in