Multiple limit cycles bifurcation from the degenerate singularity for a class of three-dimensional systems (Q272796)

The authors consider three-dimensional autonomous systems \[ {dx\over dt}= Ax+ \text{h.o.t.}, \] where the matrix \(A\) is nilpotent and has two zero eigenvalues and one negative eigenvalue. They describe procedures to determine the multiplicity of the equilibrium at the origin which provides an upper bound for the number of limit cycles bifurcating from the origin. An example is presented.