Complex dynamics in a novel jerk system with septic nonlinearity: analysis, control, and circuit realization

Abstract

Abstract This work proposes a new chaotic jerk system with septic nonlinearity. The new system presents odd symmetry and undergoes typical behaviors including period doubling, merging crisis, spontaneous symmetry breaking, coexisting attractors and coexisting bubbles of bifurcations as well. The most gratifying feature discovered in this article, is the occurrence of up to eight coexisting attractors for appropriate sets of parameters. This latter feature is uncommon for a chaotic system as simple as the model proposed in this work (e.g. not reported in cubic, quintic or hyperbolic sine models). Multistability control is achieved by following the linear augmentation approach. We numerically prove that the multistable septic chaotic system can be adjusted to develop a monostable behavior when smoothly monitoring the coupling strength. More interestingly, it is found that the coupling breaks the symmetry of the chaotic jerk system and thus induces new patterns including asymmetric Hopf bifurcations; coexisting non-symmetric bubbles, critical phenomena, coexisting multiple asymmetric attractors, just to name a few. On this line, the linear augmentation scheme can be regarded as a simple means for inducing new features in odd symmetric chaotic systems. PSPICE simulation results captured from an electronic analog of the proposed septic jerk system are consistent with the theoretical investigations.