New insights into multistability and complex resonances driven by subthreshold periodic signals in a neuronal model

Understanding how neurons respond to weak external signals is crucial for accurate signal transmission and processing in both individual nerve cells and interconnected neuronal networks. One mechanism for the detection of these responses is through resonances. In this paper, we numerically investigate the firing patterns induced in a silent Huber-Braun neuron by a sinusoidal external force. We observe complex resonance patterns, including a sequence of frequency-locking exhibited in a Devil's Staircase structure. Furthermore, we also explore the emergence of multistability induced by the nonlinear resonance. This multistability manifests as the coexistence of three attractors, such as periodic spiking, chaotic spiking, and subthreshold oscillations. The dynamical behaviors are comprehensively analyzed using time series, bifurcation diagrams, phase portraits, and the basin of attraction. In addition, we compute the maximum Lyapunov exponent to verify chaotic regimes, and estimate the fractal dimension of basin boundaries using the uncertainty exponent. We also analyze the energy consumption of resonance-induced firing patterns and coexisting attractors. The results presented in this paper have important implications for understanding the detection of subthreshold signals and the encoding of stimulus information within a neuron's firing patterns.