7. Sketch the phase-plane behavior of the following systems of linear equations and classify the stability characteristic of the steady state at (0,0): dx (a) dt dx -2у, (d) = 5x + 8y, dt dy dy —Зх — 5у. %3D = x. dt dx (e) dx = 3x + 2y, -4 – 2y, (b) dt dy Зх — у. %3D = 4x + y. dt Continuous Processes and Ordinary Differential Equations dx dx (f) = x - 4y, (c) = 2x + y, dt dt dy dy = x + y. dt = x + 2y. dt

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Q: Note: - You are attempting question 7 out of 12 dx The equilibrium points of the system =( dt a)…

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Q: a. Identify the equilibrium values. Which are stable and whichare unstable?b. Construct a phase…

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Q: Consider the following systems of rate of change equations: System A System B dx dx = 3x- dt 1 ху =…

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Q: Consider a system of two linear first-order ordinary differential equations: y1 = Y1 –- Y2, Ý2 = Y1…

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Q: characterize the equilibrium point for the system x′= Ax and sketch the phase portrait.

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Q: Sketch the phase-plane behavior of the following system of linear equations and classify the sta-…

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Q: 6. For the autonomous DE: = (y- 4)y". a. Determine equilibrium points; b. Classify each equilibrium…

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Q: sketch the phase portrait of the given system for −2 ≤ x ≤ 2, −2 ≤ y ≤ 2. Comment on the types of…

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Q: Consider the discrete model Xn+1 = -Xn- Find the equilibrium points and determine their stability.

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Q: Consider the following system of differential equations: dx dt =x−y+x2y dy dt =6x−2y−x2y. (a)…

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Q: Consider the following four nonlinear dynamic systems: a- *1 = x2, x2 = -x2 – sin (x1) b- X1 = x2,…

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Q: characterize the equilibrium point for the system x′= Ax and sketch the phase portrait.

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Q: 2. Consider the nonlinear system of differential equations dx dy = x²y – xy dt = y – e* dt (a)…

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Q: Consider the system: dx/dt=4x(1-2x)-xy dy/dt=2y-4xy (a) Are these species predator-prey or…

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Q: • Consider the following system. X = 9-1 133₂ = 34²-34-35+1 al find the equilibrium points of the…

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Q: Consider the system of differential equations dx = x + 4y dt (Σ ) : dy 2x – y dt - (i) Write the…

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Q: (4) a) Solve the initial value problem x'(t) = Ax(t), (i) 4 -5 8. A x(0) -2 1 1 Draw the phase…

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Q: 6) Consider the following model of predator-prey interaction where the prey x grows logistically in…

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Q: dx/dt=4x(1-2x)-xy dy/dt=2y-4xy (a) Find all critical (equilibrium) points. (b) Using the Jacobian…

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Q: Consider the pair of differential equations dr =1- V. dt dy = r² – y°. dt (a) Find all the…

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Q: 1. Sketch the nullclines in the xy phase plane, identify steady states, find the linearized system…

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Q: 2. Consider the system dx = -2x + y dt dy = -2y dt and its corresponding direction field. (a) Sketch…

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Q: What are the roots of the characteristic equation of the following system? dx = x – y + 4z dt dy 3x…

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Q: What are the roots of the characteristic equation of the following system? dr I - y + 4z dt dy 3x +…

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Q: For the following system: dx dt dy = x – x* dt (a) Find equilibrium point(s) of the system.

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Q: a) Show that the nonlinear dynamical system i = 2y – x² + 1, ý = 1 – x² – y? has two equilibrium…

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Q: 5- Find the differential equation for the system below. x(t) y(t) dt a) x(t) = y "(t) + (a,+a2)y…

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