3. Аnonlinear systemisdefined by the followingstatespacemodel:dx (t)-x,(t) + x3(t)= (1- x{() + xi()dtdx2(t)dtDetermine Lyapunov stability conditions for the system by utilizing Krasovskii's method.

As per the question we have a nonlinear dynamic system, and we have to determine its Lyapunov…

Answered: A nonlinear system is defined by the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For each of the nonlinear systems below, use technology to draw phase portraits (attach to the solution), determine equillibrium solutions and visually estimate whether they are stable or unstable. (a) x' = In(y + 2) x² + y (b) I' y' = y-x² - 8y² X-
Consider the system of equations dx dt dy dt a (1-33 = x 1 - y) - Y Y y (1 - 12/1 - x), 4 taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (y-)nullcline: (Enter your equation, e.g., y=x.) (Note that there are also nullclines lying along the axes.) (b) What are the equilibrium points for the system? Equilibria = (Enter the points as comma-separated (x,y) pairs, e.g., (1,2), (3,4).) (c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence: If we start at the initial position (2, 3), trajectories ? the point (Enter the point as an (x,y) pair, e.g., (1,2).)
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A nonlinear system is defined by the following state space model: dx, (t) =-x₁ (t) + x²(t) dt dx₂(t) = (1-x²(t))+ x²(t) dt Determine Lyapunov stability conditions for the system by utilizing Krasovskii's method.