4 1. Fix a value c, and then consider the one parameter family Find the value of λ (in terms of c) for which this family encounter a saddle-node bifurcation 4 1. Fix a value c, and then cons...
4. Locate the bifurcation values for the one parameter family: y = y2 - 2y + 1. Draw the phase lines for the values of the parameter smaller, larger, and equal to each bifurcation value.
In Exercises 1-6, locate the bifurcation values for the one-parameter family and draw the phase lines for values of the parameter slightly smaller than, slightly larger than, and at the bifurcation values. dy α-ly 6. dt
2(a) Consider the one-parameter family of nonlinear ordinary differential equations -Ita-) where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium solutions using appropriate arrows. ii. Find all bifurcation points and classify them 2(a) Consider the one-parameter family of nonlinear ordinary differential equations -Ita-) where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium...
Nonlinear differential equations and Bifurcation theory. Given the ordinary differential equation =1+re+ where the parameter r is a given real number. (a) Sketch all the qualitatively different vector fields that occur as r is varied. (b) Show that a saddle-node bifurcation occurs at a critical value of r, to be determined. (c) Sketch the bifurcation diagram of fixed points r* versus r.
Section B - Answer any two questions. 2. (a) Consider the one-parameter family of nonlinear ordinary differential equations dr where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium solutions using appropriate arrows. ii. Find all bifurcation points and classify them. 10 Marks (b) Consider the second order differential equation i. Show that (1) can be written as the system of ordinary differential equations (y R for...
1 y = +c is a one-parameter family of solutions for the first order DE y' + 2xy2 0. Consider the IVP consisting of the DE with the initial value y(1) = 1/4. What is the value of c? A/
Consider the following coefficient matrix, which contains a parameter a. 11 6 (a) Determine the eigenvalues in terms of α. Supposing that α > 0, enter your answers in increasing order. Equation Editor Common Ω Matrix 自0 tania) sin(a) d a 4 secia) esia)a) costa) 邇 alal sin"(a) cos-1(a) tan-"(a)- u oo Ω Matrix cosa) tana) ,..tseela, osia, =a) Va ya lal sin-(a)(a) tan ( o sinia) sec(α) //u),dx ! 읊 cscla) (b) Find the critical value or values of...
Consider a distribution with parameter λ >0 that has density f(x)= x^4/(24 λ^5) e^(-x/λ). You test the hypothesesH0:test λ =1 vs λ ≠ 1 by using the test Test: I Xbar-5 I > c. Find the smallest threshold C for an asymptotic level α
A one parameter family (with parameter c) of solutions to the problem. y'+2xy^(2)=0 is y=1/(x^2+c) (1)Find c so that y(2)=−1 c=?? 2) Find c so that y(3)=1 c??
pls choose the answer like a,b,c,d for these 5 multichoice question don't mind what i choose What can be said about the following differential equation? dy 7t It is autonomous, non-separable, linear and non-homogenous It is non-autonomous, non-separable, linear and non-homogenous It is autonomous, separable, linear and homogenous It is autonomous, separable, linear and non-homogenous. Consider the following differential equation: dt the function FA(x) -22 A, with A0, undergoes a bifurcation. Identify the type of bifurca tion. F has two...