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Download AKTU B-Tech 8th Sem 2016-17 NOE082 Non Linear Dynamics System Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 8th Semester (Eight Semester) 2016-17 NOE082 Non Linear Dynamics System Question Paper

This post was last modified on 30 January 2020

Tags:AKTUB-TechLast 10 Years2010-2020Previous Question PapersDr. A.P.J. Abdul Kalam Technical University8th Sem2016-17NOE082Non-Linear Dynamics SystemQuestion PaperPDFDownloadEngineeringExamAKTU Question Paper
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AKTU B-Tech Last 10 Years 2010-2020 Previous Question Papers || Dr. A.P.J. Abdul Kalam Technical University


Time: 3 Hours

Max. Marks: 100

Note: Be precise in your answer. In case of numerical problem assume data wherever not provided.

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SECTION-A

1. Attempt all parts of the following: (10×2=20)

  1. What is a dynamical system?
  2. What is a Strange Attractor?
  3. What are simple experiments to demonstrate chaos?
  4. What is a Cantor set?

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  5. What is an attractor?
  6. How do I know if my data are deterministic?
  7. What is quantum chaos?
  8. What are cellular automata?
  9. What are solitons?

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  10. What is spatio-temporal chaos?

SECTION-B

2. Attempt any five of the following: (10×5=50)

  1. State and explain Liapunov's theorems on (i) stability, (ii) asymptotic stability (iii) global asymptotic stability and (iv) instability.
  2. Consider the linear autonomous system:
    X' =
    0 1
    -1 -2
    X

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    Using direct method of Lyapunov, determine the stability of the equilibrium state.
  3. Explain Peano's theorem?
  4. What is the normal form theory and application to non-linear system?
  5. What is a degree of freedom?
  6. What is a Bifurcation?

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  7. Explain the control of chaos?
  8. How are maps related to flows (differential equation)? Describe the different types of solutions.

SECTION-C

Attempt any two of the following: (15×2=30)

  1. For x' = x4 - x2 + a,
    a) Sketch the phase portrait for a = 0.

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    b) How many bifurcations are taking place in this system as a function of a.
    c) In each case, determine the type of bifurcation by reducing to normal form.
    d) Draw the bifurcation diagram.
  2. For the nonlinear system given by: x' = sin y, y' = x(1 - x2),
    Answer the following questions:

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    a) How many fixed points does it have. Determine the fixed points of this system.
    b) Determine the Jacobian matrix for this system for any arbitrary fixed point (x*, y*).
    c) For the fixed points on x = 0 line, determine the type of fixed points.
    d) Draw the phase portrait ONLY around the fixed points lying on x = 0 line.
  3. What is Generic? What is the minimum phase space dimension for chaos?

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This download link is referred from the post: AKTU B-Tech Last 10 Years 2010-2020 Previous Question Papers || Dr. A.P.J. Abdul Kalam Technical University

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This post was last modified on 30 January 2020