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EOE-82: NON-LINEAR DYNAMIC SYSTEMS
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L T P
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3 1 0
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UNIT-I
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Dynamic systems:
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Concept of dynamic systems, importance of
non-linearity, nonlinear dynamics of flows (in 1,
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2, and 3 dimensions) and Maps (1 and 2 dimensions) in
phase space, Equilibrium,
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Periodicity.
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Picard’s theorem, Peano’s theorem, boundedness of
solutions, omega limit points of bounded
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trajectories.
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8
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UNIT-II
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STABILITY-I:
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Stability via Lyapunov’s indirect method, converse
Lyapunov functions, sublevel sets of
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Lyapunow functions, Lasalle’s invariance principle.
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7
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UNIT-III
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Stability-II
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Lyapunov’s direct method, converse Lyapunov’s
theorems, Brokett’s theorem, applications
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to control system, stable manifold theorem, centre
manifold theorem, normal form theory and
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applications to nonlinear systems.
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8
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UNIT-IV
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Bifurcation:
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Elementary Bifurcation theory, catastrophe, strange
attractor, fractals, fractal geometry and
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fractal dimension.
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8
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UNIT-V
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Chaos:
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Deterministic Chaos, routes to chaos (period doubling,
quasiperiodicity, intermittency,
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universality, renormalization); Measurement of Chaos
(Poincare section, Lyapunov index,
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entropy);.control of chaos.
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9
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Reference Books:
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1. D.K.
Arrowsmith and C.M. Place, “An Introduction
to Dynamical Systems” Cambridge
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University press, London, 1990.
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2. K.T.
Alligood, T.D. Sauer, and J.A Yorke, “CHAOS: An Introduction to Dynamical
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System” Springer Verlag, 1997.
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3. H.K.
Khalis, “Nonlinear Systems” Prentice Hall, 1996.
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4. R. R.
Mohler, “Non linear systems, Vol-I: Dynamics and Control” Prentice Hall,
1991.
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5. J.M. T.
Thomson and H.B. Stewart, “Nonlinear Dynamics and Chaos” John Wiley &
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Sons, 1986.
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