Research into metasurfaces is developing rapidly and is topical due to their importance and applications in various fields such as communications, cryptography, and sensing, to name a few. These materials are artificially engineered to manipulate/control electromagnetic (EM) waves, in order to present a particular functionality. In this regard, nonlinear metasurfaces may present particular functionalities that remain to be discovered. In this paper, we numerically investigate the dynamic behaviors caused by the motion of charge carriers under the intense EM field at the gap of a single nonlinear split-ring resonator (NSRR) in the terahertz (THz) frequency range. We derive the mathematical model that is used to examine the excitation properties of the NSRR and then demonstrate various tuning regions. Analysis of the two-dimensional parameter space reveals that the NSRR exhibits periodic, chaotic patterns as the amplitude of the excitation field and the loss parameter vary. However, this chaotic behavior disappears when the loss parameter is very large. The period doubling that confirms the transition between the periodic and chaotic modes is explored using the bifurcation diagram. The sensitivity of the initial conditions is examined on three dynamic region plots. Our results correctly demonstrate that the NSRR exhibits the attractive phenomenon of multistability. The coexistence of two stable states is studied and confirmed on the basin of attractions for a fixed set of amplitude or loss parameters. The energy balance of the proposed model is well analyzed on the dynamic states and parameters to characterize the different oscillation regimes. The study of the multistability in the work represents an important first step toward the development of photonic memory devices in the THz frequency range.
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