Photo from wikipedia
We study the zero-Hopf bifurcation of the third-order differential equations $$\begin{aligned} x^{\prime \prime \prime }+ (a_{1}x+a_{0})x^{\prime \prime }+ (b_{1}x+b_{0})x^{\prime }+x^{2} =0, \end{aligned}$$x″′+(a1x+a0)x″+(b1x+b0)x′+x2=0,where $$a_{0}$$a0, $$a_{1}$$a1, $$b_{0}$$b0 and $$b_{1}$$b1 are real parameters.… Click to show full abstract
We study the zero-Hopf bifurcation of the third-order differential equations $$\begin{aligned} x^{\prime \prime \prime }+ (a_{1}x+a_{0})x^{\prime \prime }+ (b_{1}x+b_{0})x^{\prime }+x^{2} =0, \end{aligned}$$x″′+(a1x+a0)x″+(b1x+b0)x′+x2=0,where $$a_{0}$$a0, $$a_{1}$$a1, $$b_{0}$$b0 and $$b_{1}$$b1 are real parameters. The prime denotes derivative with respect to an independent variable t. We also provide an estimate of the zero-Hopf periodic solution and their kind of stability. The Hopf bifurcations of these differential systems were studied in [5], here we complete these studies adding their zero-Hopf bifurcations.
Journal Title: Differential Equations and Dynamical Systems
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!