Concept explainers
Interpretation:
To show there is always unstable fixed point at
Concept Introduction:
To check the stability at any point, differentiate the equation and put the value in it.
For small value of x predation is very weak, thus the budworm population increases exponentially, when
Answer to Problem 1E
Solution:
Instability at
Explanation of Solution
Given information:
The given expression is dimensionless for budworm population growth
Where
To check the stability of the equation at
By substituting
Given condition is
This result is also verified by plotting graph for equation
From the above graphs, it is clear that for
For the given type of system, there is always an unstable fixed point at
Want to see more full solutions like this?
Chapter 3 Solutions
Nonlinear Dynamics and Chaos
- (a) Define the notion of an ideal I in an algebra A. Define the product on the quotient algebra A/I, and show that it is well-defined. (b) If I is an ideal in A and S is a subalgebra of A, show that S + I is a subalgebra of A and that SnI is an ideal in S. (c) Let A be the subset of M3 (K) given by matrices of the form a b 0 a 0 00 d Show that A is a subalgebra of M3(K). Ꮖ Compute the ideal I of A generated by the element and show that A/I K as algebras, where 0 1 0 x = 0 0 0 001arrow_forward(a) Let HI be the algebra of quaternions. Write out the multiplication table for 1, i, j, k. Define the notion of a pure quaternion, and the absolute value of a quaternion. Show that if p is a pure quaternion, then p² = -|p|². (b) Define the notion of an (associative) algebra. (c) Let A be a vector space with basis 1, a, b. Which (if any) of the following rules turn A into an algebra? (You may assume that 1 is a unit.) (i) a² = a, b²=ab = ba 0. (ii) a² (iii) a² = b, b² = abba = 0. = b, b² = b, ab = ba = 0. (d) Let u1, 2 and 3 be in the Temperley-Lieb algebra TL4(8). ገ 12 13 Compute (u3+ Augu2)² where A EK and hence find a non-zero x € TL4 (8) such that ² = 0.arrow_forwardQ1: Solve the system x + x = t², x(0) = (9)arrow_forward
- Between the function 3 (4)=x-x-1 Solve inside the interval [1,2]. then find the approximate Solution the root within using the bisection of the error = 10² method.arrow_forwardE10) Perform four iterations of the Jacobi method for solving the following system of equations. 2 -1 -0 -0 XI 2 0 0 -1 2 X3 0 0 2 X4 With x(0) (0.5, 0.5, 0.5, 0.5). Here x = (1, 1, 1, 1)". How good x (5) as an approximation to x?arrow_forwardby (2) Gauss saidel - - method find (2) و X2 for the sestem X1 + 2x2=-4 2x1 + 2x2 = 1 Such thef (0) x2=-2arrow_forward
- ax+b proof that se = - è (e" -1)" ë naxarrow_forward20.11 ← UAS Sisa waktu 01:20:01 51%- Soal 2 Perhatikan gambar di bawah (Sembunyikan ) Belum dijawab Ditandai dari 1,00 5 A B E D 10 20 Jika ruas garis AB, PE, dan DC sejajar dan ketiganya tegak lurus dengan ruas garis BC, maka panjang ruas garis PE adalah ... (cukup tulis bilangannya tanpa spasi dalam bentuk desimal tiga angka di belakang koma, seperti a,bcd atau pecahan m/n untuk m n Jawaban: Jawaban ||| <arrow_forward20.07 52% X https://www.chegg.com/hc <: C Chegg Learn on the go = Chegg (X) Open in app EN-US ✔ What's your next question? √x #16 A surveyor sees a building across the river. Standing at point A he measures the angle of elevation from the ground to the top of the building to be 30 degrees. He steps back 100 feet and again measures the angle of elevation and finds it to be 15. (See Figure 12.26.) Assuming that it makes a 90-degree angle with the floor, approximately how tall is the building? 15 30° 100 A river Figure 12.26 Show image transcript Here's the best way to solve it. Solution ||| о building < Sharearrow_forward
- No chatgpt pls will upvotearrow_forwardModule Code: MATH380202 3. (a) Let {} be a white noise process with variance σ2. Define an ARMA(p,q) process {X} in terms of {+} and state (without proof) conditions for {X} to be (i) weakly stationary and (ii) invertible. Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q) process and show how it can also be represented as an ARMA process, giving the AR and MA orders of this representation. (b) The following tables show the first nine sample autocorrelations and partial auto- correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice that the notation in this part has no relationship with the notation in part (a) of this question.) Identify a model for this time series and obtain preliminary estimates for the pa- rameters of your model. X₁ = 15.51, s² = 317.43. k 1 2 3 4 5 6 7 Pk 0.981 0.974 0.968 akk 0.981 0.327 8 9 0.927 0.963 0.957 0.951 0.943 0.935 0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012 Y₁ = VX : y = 0.03, s² = 11.48. k 1…arrow_forwardLet G be a graph with n ≥ 2 vertices x1, x2, . . . , xn, and let A be the adjacency matrixof G. Prove that if G is connected, then every entry in the matrix A^n−1 + A^nis positive.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning