Question 1 Consider the logistic map with parameter $x_{n-1} = \frac{5}{2}x_n(1 - x_n)$ (a) Find all the equilibria and determine their stability. (b) Produce a cobweb plot to verify the stability and type of each equilibrium.
Added by Shane N.
Close
Step 1
Step 1: To find the equilibria, we set $x_{n-1} = x_n = x$ and solve for $x$. Show more…
Show all steps
Your feedback will help us improve your experience
Shaiju T and 57 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
(a) Use the stability criterion to characterize the stability of the equilibria of $$x_{t+1}=\frac{5 x_{t}^{2}}{4+x_{t}^{2}}, \quad t=0,1,2, \ldots$$ (b) Use cobwebbing to find the limit that $x_{t}$ converges to as $t \rightarrow \infty$ if (i) $x_{0}=0.5$ and (ii) $x_{0}=2$.
Shaiju T.
Answer ALL parts (a) to (c) of this question. Consider the following non-linear first order planar system of difference equations: dot{x} = 2x - x^2 - xy dot{y} = -y + xy (a) [10 marks] Compute the steady states. (b) [25 marks] Linearize the system around the steady state(s) with x ≠0, y ≠0 and asses the(ir) stability. (c) [15 marks] Draw the phase diagram for this dynamical system.
Adi S.
Question 8. [10 points] Consider the following difference equation xt+1 = axt / (b + xt) = f(xt), a, b > 0. (a) [4 points] Find all of equilibria for the given equation. (b) [6 points] For a = 5, b = 3, use the cobwebbing method to sketch the approximate behavior of solutions to the equation from initial values x0 = 1 and x0 = 3. What conclusion can you draw about the long term behavior of solutions?
Madhur L.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD