ZERO-HOPF BIFURCATION IN NUCLEAR SPIN GENERATOR SYSTEM

By computing we obtain that P-1(0, 0, 1) is a zero-Hopf equilibrium point of nuclear spin generator system. We prove that there exist two families of nuclear spin generator system which has the zero-Hopf equilibrium point P-1(0, 0,1). Furthermore we prove that a limit cycle bifurcated from P-1(0, 0,1) by averaging method of one order and second order respectively.

Automated summary

Through computation, we have identified P-1(0,0,1) as a zero-Hopf equilibrium point in the nuclear spin generator system. Furthermore, we have proven the existence of two families of nuclear spin generator systems with this equilibrium point, as well as the bifurcation of a limit cycle from P-1(0,0,1) using first and second order averaging methods.