EBK NONLINEAR DYNAMICS AND CHAOS WITH S
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
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Chapter 7.2, Problem 13E
Interpretation Introduction

Interpretation:

It is to be shown using Dulac’s criterion with the weighing function g = (N1N2)1, the system

N˙1= r1N1(1 - N1K1) - b1N1N2, N˙2= r2N2(1 - N2K2) - b2N1N2 has no periodic orbits in the first quadrant N1,N2 > 0.

Concept Introduction:

The method for ruling out closed orbits, that is, ruling out the existence of a limit cyclebased on Green’s theorem, is called Dulac’s criterion.

Consider a continuously differentiable vector field x˙ = f(x) distinct on a subset R of the plane. If a continuously differentiable function, real valued function g(x) and if .(g(x˙)) has same sign throughout subset R, then there will not be any closed orbit lying entirely in R.

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