The suitable Liapunov function for the systema) V(x, y) = x² + y²b) V(x, y) = x² + 2y²c) V(x, y) = 2x² + y²d) V (x,y) = 1⁄2 x² + y²dxdt=−x³ + xy²,dt= -2x²y - y³ is

Answered: Image /qna-images/answer/015b6a4c-de4b-47f2-80a0-646ff2025a1e.jpg

Answered: The suitable Liapunov function for the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

A student correctly obtained the following characteristic equation: 2x² -4x2 +7x =0 What homogeneous linear equation is this student solving? O 2x³y" – 4x²y" +7xy=0 O 2y" – 4y"+7=0 O 2y" - 4y" +7y' = 0 o dy -2x³ – 4x² +7x 3D2X3 dx « Previous Not a 98
a) Which of the following systems of ODEs is autonomous and dynamical? III, II where 1: y₁= e = sin(y2), y2 = ₁ + y2 II: dy dy₁ dx dy₂ = 5y₁, y = dx Y₂' = V1 Y2 - y2 1 III: Y1 = Зуг, = -12 b) Find out which of the following options are equilibria of the dynamical system, IV where I:(y₁, y) = (5,0); II:(y₁, y₂) = (3,0); III:(y₁, y) = (0, 1); IV:(y₁, y) = (3,2). y₁ = ₁₂ - 1, y2 = (y₁ - 3)y2 =
Write the system of equations in the image in matrix form
A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chessboard. On the second square, the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed on a square 16? Also, find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pounds.)
5. Okay, time for some mathematics. We're going to focus on the interactions between the hares and their main predators, the lynx. The tool we need is differential equations (last seen when we talked about the S-I-R disease model). We will let H(t) be the density of hares at time t, and L(t) the density of lynx at time t. Our first assumption is that, if there are no lynx around, the hares grow exponentially. Hares lead to more hares and faster growth. This gives us the differential equation (trust me): HP = aH dt where a is a positive constant. Second we assume that, if there are no hares around, the lynx starve and thus their numbers decay exponentially. This gives us: TP = -bL dt

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

The suitable Liapunov function for the system a) V(x,y) = x² + y² b) V (x,y) = x² + 2y² c) V (x, y) = 2x² + y² d) V(x,y) = 1⁄2 x² + y² dt +xy², dt = -2x²y-y³ is