For the given function x ˙ = r-x-e -x and x ˙ = 1-x-e -rx the value of r at which bifurcation occurs is to be determined. The bifurcation is to be classified as saddle-node, trans-critical, supercritical pitchfork, or subcritical pitchfork. The bifurcation diagram of fixed points is to be sketched. Concept Introduction: Bifurcation theory is used to the study of the stability of the dynamical system. Small blank dot is used for unstable point and the black dot represents at that point, the system is stable. Dotted line and dark line represent that system is unstable and stable respectively.

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Chapter 3.4, Problem 13E

Interpretation Introduction

Interpretation:

For the given function x˙= r-x-e-x and x˙= 1-x-e-rx the value of r at which bifurcation occurs is to be determined. The bifurcation is to be classified as saddle-node, trans-critical, supercritical pitchfork, or subcritical pitchfork. The bifurcation diagram of fixed points is to be sketched.

Concept Introduction:

Bifurcation theory is used to the study of the stability of the dynamical system.

Small blank dot is used for unstable point and the black dot represents at that point, the system is stable. Dotted line and dark line represent that system is unstable and stable respectively.

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