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I have to study the presence of an Hopf Bifurcation in a dynamical system with 4 equations. I have found a criterion of Hopf bifurcation without using eigenvalues, in which the bifurcation is called SIMPLE Hopf bifurcation because a condition is that all the eigenvalues must appear with non negative real part. Is there any criterion for obtaining Hopf bifurcations without using eigenvalues? So I could locate the presence of the traditional Hopf bifurcation, not only the SIMPLE one. Thanks.

asaadadd
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  • Could you explain your question? What do you mean by "I have found a criterion of Hopf bifurcation without using eigenvalues", if you said that the criterion is that all eigenvalues have non negative real part? – yohBS Feb 20 '13 at 14:31
  • The criterion I am talking about can be found in the free .pdf
    "Criterion of Hopf Bifurcations without Using Eigenvalues" by Liu     – asaadadd Feb 20 '13 at 14:43

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Detailed information on this criterion can be found in the book: Time and Space in Economics. For a computational implementation, you can refer to the work I published not long ago in the Wolfram Function Repository: BialternateSum.

E. Chan-López
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