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A note on Hopf bifurcation in Chen’s system. (English) Zbl 1074.34045

Chen’s system \(\dot x= a(y- x)\), \(\dot y= cx- xz- y\), \(\dot z= xy- bz\), is considered under the conditions \(b= \frac{17}{8}c\), \(a= \frac 34c\). The Andronov-Hopf bifurcations of the equilibria are calculated and their character (supercriticality, resp subcriticality) is determined.

MSC:

34C23 Bifurcation theory for ordinary differential equations
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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