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

EOE-82: NON-LINEAR DYNAMIC SYSTEMS

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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.

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UNIT-II

STABILITY-I:

Stability via Lyapunov’s indirect method, converse Lyapunov functions, sublevel sets of

Lyapunow functions, Lasalle’s invariance principle.

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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.

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UNIT-IV

Bifurcation:

Elementary Bifurcation theory, catastrophe, strange attractor, fractals, fractal geometry and

fractal dimension.

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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.

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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