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| Paper IPM / M / 18022 |
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| Abstract: | |||||
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This paper explores the simplest truncated orbital and parametric normal forms
of controlled Hopf zero singularities. We assume a quadratic generic condition
and complete the remaining results on their simplest truncated orbital and
parametric normal forms of Hopf-zero singularities. Different normal form
styles are explored for their potential applications in bifurcation control. We
obtain their associated universal asymptotic unfolding normal forms. We derive
coefficient normal form formulas of the most generic cases and present the relations
between the controller coefficients and asymptotic universal unfolding
parameters. These play an important role in their potential applications in
bifurcation control. Finally, the results are implemented on a controlled Chua
circuit system to illustrate the applicability of our results.
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