<p>This paper investigates the complex bifurcation mechanism and chaotic characteristics of a four-dimensional hyperjerk system with novel chains of bubbles. The parameter-dependent normal forms for the codimension 2 Bogdanov-Takens bifurcation of the system are explored. We establish the accurate relationships among system parameters at different bifurcations including pitchfork bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. The obtained bifurcation values can be used in the controller or observer applied to appropriate input, which can realize the multistate switching control of the circuit model. Furthermore, the analysis carried out in this work reveals period-doubling bifurcations, controllable antimonotonicity, bursting oscillations, initial-associated coexisting behaviors and boundary crisis in numerical simulations. Of most distinctive and rare is the finding of one to three full Feigenbaum remerging trees and serial chains of bubbles under parameters control. In addition, we observed that the frequency and phase of the system experience a period of frequency and phase fluctuations to approach the locking state, which can be divided into three stages: the slipping stage, jump stage and the oscillation stage. The jump dynamics with initial sensitivity are also traced and controllable. These performance analysis of hyperjerk circuit system provide theoretical support, and can strongly enhance the security since a tiny change in circuit parameters and initial conditions will influence the whole encryption or electroacupuncture treatment process.</p>