To compute Lorenz map for r = 28 , σ = 10 , b = 8 / 3 using numerical integration. Concept Introduction: ➢ Lorenz equations x ˙ = σ ( y − x ) y ˙ = rx − y − xz z ˙ = xy − bz Here σ, r, b > 0 The solution of Lorenz equations oscillates irregularly for a wide range of parameters, never exactly repeating, but it always remains in a bounded region of phase space. ➢ Strange attractor: It is not the same as a fixed point, limit cycle, a point, a curve or surface. It is a fractal having fractional dimensions between 2 and 3 . ➢ Chaos: It is the study of deterministic differential equations that display sensitive dependence on initial conditions.

Question

Want to see the full answer?

Answer 1

Question

Chapter 9.4, Problem 1E

Interpretation Introduction

Interpretation:

To compute Lorenz map for r=28,σ=10,b=8/3 using numerical integration.

Concept Introduction:

➢ Lorenz equations

x˙=σ(y−x)y˙=rx−y−xzz˙=xy−bzHere σ, r, b > 0

The solution of Lorenz equations oscillates irregularly for a wide range of parameters, never exactly repeating, but it always remains in a bounded region of phase space.

➢ Strange attractor: It is not the same as a fixed point, limit cycle, a point, a curve or surface. It is a fractal having fractional dimensions between 2 and 3.

➢ Chaos: It is the study of deterministic differential equations that display sensitive dependence on initial conditions.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Page < 1 of 2 - ZOOM + 1) Answer the following questions by circling TRUE or FALSE (No explanation or work required). −1 0 01 i) If A = 0 0 2 0, then its eigenvalues are ₁ = 1,λ₂ = 2, and 13 0 0 = : 0. (TRUE FALSE) ii) A linear transformation is operation preserving because the same result occurs whether you perform the operations of addition and scalar multiplication before or after applying the linear transformation. ( TRUE FALSE) iii) A linear transformation that is one-to-one and onto is called an isomorphism. (TRUE FALSE) iv) If the standard matrix A for the linear transformation T: R³ → R³ is -1 0 01 A = 2 00, then T is invertible. (TRUE FALSE) 0 1 1. v) Let A, B, and C be square matrices of order n. If A is similar to B and B is similar to C, then A is similar to C. ( TRUE FALSE) 2) a) i) Find the matrix that produces the counterclockwise rotation of 30° about the z-axis. ii) Find the image of the vector (1,1,1) for the rotation described in i). b) Give a geometric description…

Pls help ASAP

1. Except for the door and floor, a shed is built entirely out of plywood. How many square meters of plywood are needed to build the shed? (1 foot 0.3048 m) 10 ft. 7 ft. 3 ft. 18 ft. 17 ft. 15 ft.