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 collection of trajectories in a phase plane is called as phase portrait.
The point which satisfies the condition
Closed Orbit corresponds to 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 a unstable fixed point.
If nearby trajectories moving away from the fixed point then the point is said to be unstable fixed point.
If nearby trajectories moving towards the fixed point then the point is said to be stable fixed point.
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
- The amount of heat H (in joules) required to convert one gram of water into vapor is linearly related to the temperature T (in C) of the atmosphere. At 10C this conversion requires 2480 joules, and each increase in temperature of 15C lowers the amount of heat needed by 40 joules. Express H in terms of T.arrow_forwardSophia has already prepared 1 kilogram of dough and will continue preparing 1 kilogram of dough every hour write an equation that shows the relationship between the hours work x and the dough prepared yarrow_forwardfind the value of y when x=1arrow_forward
- The pollution level in the center of a city at 4am is 22 parts per million and it grows in linear fashion by 19 parts per million every hour. If y is pollution and t is time elapsed after 4am, A. Determine the equation that relates y with t. B. What is the pollution level at 2:30pm?arrow_forwardThe equation of motion of a particle is s= t3- 3t , where sis in meters and is in seconds. Find(a) the velocity and acceleration as functions of ,(b) the acceleration after 2 s, and(c) the acceleration when the velocity is 0.arrow_forwardFind the equation of the line perpendicular to 8x + 2y = 1 passing through the point (4, –1). y = -Xarrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningElementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice UniversityCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,