Bifurcation structures in three unidirectionally coupled electromechanical systems with no external signal and with regenerative process

Abstract

We study the bifurcation structures in three unidirectionally coupled nonlinear electromechanical systems (EMS) with no external signal. The coupling between the systems is realized with integrator operational amplifiers. It is found that the magnetic field and the damping coefficient control the appearance of Hopf bifurcation. By varying the coupling coefficient, various dynamical behaviors corresponding to different types of bifurcation are observed. A special case having one linear EMS unidirectionally coupled to two nonlinear EMS also shows a series of bifurcation leading to periodicity, quasiperiodicity, chaos, hyperchaos and then again periodic states. Finally taking into consideration a time delay due to regenerative process, it is found that for small time delay and regenerative process strength, the system remains motionless, leading to periodic oscillation at critical value, then quasiperiodicity, chaos and instability as the delay and the regenerative process strength increase.