HOPF BIFURCATION ANALYSIS AND AMPLITUDE CONTROL OF A NEW 4D HYPER-CHAOTIC SYSTEM

Abstract

Hopf bifurcation and amplitude control in a new 4D hyper-chaotic system are investigated in this paper.  Theoretical analysis shows that the system will exhibit Hopf bifurcation at equilibrium when the Hopf bifurcation conditions are satisfied.  Relationship between the amplitude and control gains is given.  Hence the amplitude of the limit cycle can be controlled by choosing suitable control gains, ensuring the stability of the bifurcating period solution.  Finally, some applications of the amplitude control are carried out to illustrate the effectiveness of the main theoretical results.  The accuracy of different kinds of control function are also compared.