Dynamical behaviors of a complex-variable laser system with a memcapacitor

The memcapacitor is integrated into a nonlinear system to enhance its nonlinear dynamical characteristics and to capture the effect of external electric-field. This paper proposes a novel complex-variable laser system incorporating a memcapacitor (MCVLS). The energy function of the MCVLS is derived using the Helmholtz’s theorem. Furthermore, the hidden dynamical behaviors of the MCVLS, which depend on parameters, time and initial conditions, are systematically investigated. The results demonstrate that the MCVLS can generate rich dynamical behaviors under different parameter settings, including hidden multi-scroll attractors exhibiting spiking or bursting patterns. A negative correlation is observed between the system energy and the number of scrolls, suggesting that scroll generation consumes energy. In particular, by adjusting the two initial conditions of the memcapacitor, hidden two-dimensional (2-D) offset-boosting coexisting attractors with hybrid-topology can be generated, each exhibiting distinct offset trajectories. Notably, the system exhibits complex hidden neuromorphic firing behaviors such as spiking and bursting, including an exceptionally rare time-originated firing transitions that involves three distinct firing patterns. These findings hold promising potential for applications in the fields of information security and optical brain-like computing.