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Interpretation:
To show by using Poincare-Bendixson Theorem that the system has at least one periodic solution.
Concept Introduction:
Poincare-Bendixson Theorem: If
R is a closed, bounded subset of the plane
R doesn’t contain any fixed points
There exists a trajectory C that is confined in R, in the sense that it starts in R and stays in R for all future time whether C is closed orbit, or it spirals towards a closed orbit as
To check the stability of fixed point use Jacobian matrix
The point
Relation between polar and Cartesian
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Chapter 7 Solutions
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
- Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by the parametric representation x1=t, x2=s and x3=3+st, where s and t are any real numbers. Then show that the solutions to the system can also be written as x1=3+st,x2=s and x3=t.arrow_forwardConsider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the system have exactly one solution?arrow_forwardSolve Exercise 14 if a 25 solution of the same mixture is added instead of pure alcohol.arrow_forward
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