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

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B. TECH.
THEORY EXAMINATION (SEM?VIII) 2016-17
NON-LINEAR DYNAMICS SYSTEM
T ime : 3 Hours Max. Marks : 100
Note .' Be precise in your answer. In case ofnumericalproblem assume data wherever not provided.
SECTION-A
1. Attempt all parts of the following- (10X2=20)
a. What is a dynamical system?
b. What is a Strange Attractor?
e. What are simple experiments to demonstrate chaos?
d. What is a Cantor set?
e. What is an attractor?
f. How do I know if my data are deterministic?
g. What is quantum chaos?
h. What are cellular automata?
i. What are solitons?
j. What is spatio?temporal chaos?
SECTION-B
2. Attempt any ?ve of the following: (10><5=50)
a) State and explain Liapunov?s theorems on (i) stability, (ii) asymptotic stability (iii) global
asymptotic stability and (iv) instability.
b) Consider the linear autonomous system
' i 0 1 i
X = X
?1 ? 2
Using direct method of Lyapunov, determine the stability of the equilibrium state.
e) Explain Peano?s theorem?
d) What is the normal form theory and application to non?linear system?
e) What is a Bifurcation?
1) What is a degree of freedom? How are maps related to ?ows (differential equation)?
g) Explain the control of chaos?
h) Describe the different types of solutions.
SECTION-C
Attempt any two of the following: (15X2=30)
3. F0rx'=x4?x2+a,
3) Sketch the phase portrait for (x = 0.
b) How many bifurcations are taking place in this system as a function of 0.
c) In each case, determine the type of bifurcation by reducing to normal form
d) Draw the bifurcation diagram.
4. for the nonlinear system given by: x' = sin y, y? = x(l ? x 2 ),
Answer the following questions:
a) How many fixed points does it have. Determine the ?xed points of this system.
b) Determine the J acobian matrix for this system for any arbitrary fixed point (x * , y* ).
e) 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.
5. What is Generic? What is the minimum phase space dimensmn tor chaos?
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