Question: . Consider the ODE system i = x(1 -x2) y = -y. Show that any rectangle of the form [-a, a] x [-b, b] with

. Consider the ODE system i = x(1 -x2) y = -y. Show that any rectangle of the form [-a, a] x [-b, b] with a 2 1 and b > 0 is a trapping region. Argue why this yields global existence (forward in time) for any choice of initial data

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Let w1, w2 R and let the ODE system be x = 81x2, x2 = -w1x1, y = W2y2, 32 = -W241. Do not solve the EDO. a) Find three non-trivial prime integrals that are two by two linearly independent. b) We...

2. In this problem we are given the location of each object and the type of object (triangle, circle or square) along with an identifying name (e.g., T1, C1, S1). The data is tabulated below. The...

Consider the linear program max x 1 + x2 s.t. x1 + x2 9 -2x1 + x2 0 x1 - 2x2 0 x1, x2 0 (a) Solve the problem graphically. (b) Add slacks x3,c, x5 to place the model in standard form. (c) Apply...

9/14/10 12:39 PM Page 381 Chapter dug84356_ch06a.qxd 6 Rational Expressions Advanced technical developments have made sports equipment faster, lighter, and more responsive to the human body. Behind...

3 Systems of differential equations Theorem 3. Any n linearly independent vectors in an n dimensional space V must also span V. That is to say, any n linearly independent vectors in an n dimensional...

Downloaded 02/28/15 to 132.174.255.3. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php 15.7. Exercises 475 changes and we laugh no more. While...

Math 400 Assignment #3 -- Numerical Integration and Differentiation 1. For the function g x e x 2 2 Due: 6am April 09, 2016 use the centered difference formula with h 101 , 102 , , 1020 to create a...

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

5. (20%) A solar collector made of aluminum with black coating is placed on the roof with a tilt degree of 45 with respect to the floor. The length of the solar collector is Im. The solar...

Refer to the information provided for Peach Computer in E1111. In E1111, Portions of the financial statements for Peach Computer are provided below. Required: Prepare the operating activities section...

One of the important values of credit default swaps is that they allow Fis to hedge risk, which is more likely to cause an Fi to fail than either interest rate risk or foreign exchange risk....

A company issues 1,050 shares of its common stock for $33,600 cash. Prepare journal entries to record this event under each of the following separate situations.