H2. Classify the critical point and sketch the phase portrait of the following systems of first order equations dx = x+3y, dt dx — 5х — у, { { (i) (ii) dy = 3x+y; dt dy 3x+y. dt

Q: 3. For the competing species population model dx —D х(-х — Зу + 150) dt dy %3D У(-2х — у + 100) dt…

A:

Q: Determine the local stability of equilibrium of the predator prey model x(t) = x -0.5xy (t) = 3xy —…

A:

Q: For the following systems, find th

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Write the given second order equation as its equivalent system of first order equations. u" – 7.5u'…

A: Given second order differential equation is u''-7.5u'+1.5u=-3sin(3t)...(1), u(1)=0 and u'(1)=1.5.

Q: a) Which of the following systems of ODES is autonomous and dynamical? where ty₁ = e-sin(₂), y₂ = ₁…

A:

Q: Consider the autonomous first order equation y' = y° + 3y³ – 10y*.

A:

Q: For the each of the following autonomous equations, find all the equilibrium solutions. For each…

A: Equilibrium solutions for autonomous differential equations occur where the derivative y' is equal…

Q: Consider the system of differential equations: dx 2x – Y dt dy 5x – 2y dt Plot a well-labeled phase…

A: Consider a given system of ordinary differential equation: dxdt=2x-ydydt=5x-2y Plot a well-labelled…

Q: d.S dt dI dt = TI - PSI, pSI – TI, where I represents individuals who are infected with some virus…

A: The system of differential equations given describes a simplified model of disease spread.The…

Q: 3 please

A: Step 1:3.To sketch the phase portrait, we need to consider cases for ( α ) greater than, less than,…

Q: Consider the system x ' - x = u ( t ) . Can one steer 1 to 0 by a differentiable control function u…

A: Yes, it is possible to steer the state variable (x) from 1 to 0 by choosing an appropriate…

Q: (1) Show that the system x=-2 cos x - cos y y=-2 cos y - cos x is reversible but not conservative.…

A: To show that the system is reversible but not conservative.And to plot the phase portrait

Q: de Consider a model: = 1- cos 0 – ÷(1 + cos 0) dt (a) Determine the equilibrium points for this…

A: We are given, dθdt=1-cosθ -13(1+cos θ) Condition of Equilibrium: dθdt=0 ⇒1-cos θ-13(1+cos θ)=0⇒1-cos…

Q: Which of the following functions (y1, y2) is a Lyapunov function for the dynamical system y₁ = - Y₁…

A: Which of the following function Vy1 , y2 is the Lyapunov function for the dynamic system? y1˙=-y1y22…

Q: Find the general solution and draw the phas (a) [] d dt y 2 x

A:

Q: 1) Write the given second order equation as its equivalent system of first order equations. u"…

A:

Q: H1. Find the equilibria and determine their stability using linear stability analysis for the…

A: The objective of the question is to find the equilibrium points and determine their stability for…

Q: Consider the system dx/dt = x(2-x-y) dy/dt = y(y-x2) a. Determine and sketch the…

A: Given: dxdt = x(2-x-y) dydt = y(y-x2) for the nullclines. dxdt = x(2-x-y)=0 x=0 (or) y=2-x------(1)…

Q: Consider the system dx/dt = -x dy/dt = -4x3+y a. show that the origin is the only equilibrium…

A:

Q: Find the order of the given DE. Also, decide if the DE is linear or nonlinear. (a) + yx = x (b) 1-…

A: The differential equation dydx+y2x=x contains the highest derivativedydx which is of first order.…

Q: Consider the system dx/dt = -x dy/dt = -4x3+y a. show that the origin is the only equilibrium…

A:

Q: 1) Find the equilibra and sketch the phase line of the autonomous ODE u' = u*(2 – u). Determine the…

A: