Concept explainers
Interpretation:
Find the fixed points and classify them, sketch the neighboring trajectories.
Concept Introduction:
The parametric curves traced by solutions of a differential equation are known as trajectories.
The geometrical representation of a collection of trajectories in a phase plane is called a phase portrait.
The point which satisfies the condition
Closed Orbit corresponds to the periodic solution of the system i.e.
If nearby trajectories moving away from the fixed point then the point is said to be saddle point.
If the trajectories swirling around the fixed point then it is an unstable fixed point.
If nearby trajectories moving away from the fixed point then the point is said to be saddle point.
If the trajectories swirling around the fixed pointthen it is an unstable fixed point.
To find the fixed point of the system put
To check the stability of fixed-point use Jacobian matrix
The point
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
- Trace the curve x3y − x − 1 = 0.arrow_forwardPlease don't provide handwritten solution .....arrow_forwardA Ferris wheel has a diameter of 40 meters and rotates at a constant speed completing one full revolution every 2 minutes. If a person gets on the Ferris wheel at the bottommost point, express the person's height above the ground as a function of time, assuming the center of the Ferris wheel is at ground level. Answer: The Ferris wheel has a diameter of 40 meters, which means the radius (r) is half of the diameter, i.e., (r = 20) meters. The Ferris wheel completes one full revolution every 2 minutes. The period (T) of the Ferris wheel is the time it takes to complete one full revolution. In this case, T = 2 minutes. The angular frequency (w) can be calculated using the formula (w = 2/?). Substituting the given value for (T): w = 2/? = ? radians per minute. Now, the height (h) of the person above the ground as a function of time (t) can be expressed using a sine function. The general form of a sine function is h(t) = A sin(wt+ϕ)+C where: - A is the amplitude (half the range of the…arrow_forward
- Elementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice UniversityGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill