• www.uptuexam.com
  • GBTU Results 2014
  • MTU Results 2014
  • UPTU Circulars
  • COP Result 2012,13,14
  • UPTU Previous Papers
  • GATE study material
  • Robotics Projects
Thank you for visiting www.UPTUexam.com " Free download Exam materials, previous year question papers, free ebooks & Providing Important Questions To Do their Exams Well and Totally a FREE SERVICE for all engineering streams (B.Tech)."

GBTU / MTU Syllabus of NON-LINEAR DYNAMIC SYSTEMS [Effective from the session : 2012-13]

EOE-82: NON-LINEAR DYNAMIC SYSTEMS

L T P
3 1  0
UNIT-I
Dynamic systems:
Concept of dynamic systems, importance of non-linearity, nonlinear dynamics of flows (in 1,
2, and 3 dimensions) and Maps (1 and 2 dimensions) in phase space, Equilibrium,
Periodicity.
Picard’s theorem, Peano’s theorem, boundedness of solutions, omega limit points of bounded
trajectories.
8
UNIT-II
STABILITY-I:
Stability via Lyapunov’s indirect method, converse Lyapunov functions, sublevel sets of
Lyapunow functions, Lasalle’s invariance principle.
7
UNIT-III
Stability-II
Lyapunov’s direct method, converse Lyapunov’s theorems, Brokett’s theorem, applications
to control system, stable manifold theorem, centre manifold theorem, normal form theory and
applications to nonlinear systems.
8
UNIT-IV
Bifurcation:
Elementary Bifurcation theory, catastrophe, strange attractor, fractals, fractal geometry and
fractal dimension.
8
UNIT-V
Chaos:
Deterministic Chaos, routes to chaos (period doubling, quasiperiodicity, intermittency,
universality, renormalization); Measurement of Chaos (Poincare section, Lyapunov index,
entropy);.control of chaos.
9
Reference Books:
1.   D.K. Arrowsmith and C.M. Place, “An Introduction  to Dynamical Systems” Cambridge
University press, London, 1990.
2.   K.T. Alligood, T.D. Sauer, and J.A Yorke, “CHAOS: An Introduction to Dynamical
System” Springer Verlag, 1997.
3.   H.K. Khalis, “Nonlinear Systems” Prentice Hall, 1996.
4.   R. R. Mohler, “Non linear systems, Vol-I: Dynamics and Control” Prentice Hall, 1991.
5.   J.M. T. Thomson and H.B. Stewart, “Nonlinear Dynamics and Chaos” John Wiley &
Sons, 1986.
6.   Stanislaw H. Zak, “Systems and control” Oxford University Press, 2003

No comments:

Post a Comment

Google+ Followers