Nonlinear dynamics of Hodgkin-Huxley neurons

Dynamika nieliniowa neuronów Hodgkina-Huxleya This monograph describes the dynamics of the Hodgkin-Huxley neurons stimulated by periodic and stochastic stimuli. In the high frequency regime there is a multimodal transition between the odd-only modes and the state with both odd and even modes. This singularity appears in the presence of noise as a stochastic anti-resonance. The competition of different parity modes is also reflected in the structure of the resonances, where even and odd phase-locked states are separated by crossover regimes. The boundaries between various mode-locked states form complicated patterns. The relation between the output frequency and stimulus amplitude near the excitation threshold is often continuous even in the absence of noise. Several scaling relations are found. Models of regular spiking excitatory and inhibitory cells of mammalian cortex are also studied within this framework. The obtained high variability of response agrees with experiments in vivo.