This study proposes a switchable memristor to simulate autapse in the Hindmarsh-Rose (HR) neuron model, and introduces a flux-controlled memristor to model the effect of electromagnetic radiation. The proposed 4D HR neuron model without equilibrium points exhibits complex hidden firing activities, which are analyzed through phase diagrams, time series, bifurcation diagrams, Lyapunov exponent spectrums, and two-parameter dynamical maps. The memory attributes of the memristive autapse play a crucial role in the firing activities of the neuron, enabling transitions between periodic spiking with different frequencies and chaotic firing. Additionally, the transition between periodic and chaotic firing induced by the initial value of the switchable memristor is also discovered when it is configured as three different types of memristors. A neuron circuit is designed with current-mode devices to improve accuracy and reduce power consumption. Multisim simulation results are provided to validate the correctness of the neuron model and the effectiveness of numerical analysis. The switchable memristor can exhibit three different memory attributes by controlling the parameter m: nonvolatile discrete memory (m=1), nonvolatile continuum memory (m=0.5), and volatile memory (m=0.25). The study reveals that the firing patterns of the neuron are significantly influenced by the memory attributes of the memristive autapse, and the neuron exhibits different firing patterns when the switchable memristor is configured as different memory states. The results demonstrate that the neuron is sensitive to the initial conditions of the memristive autapse, and the firing patterns can transition without system parameters. The proposed model and circuit design provide a new approach for simulating neuronal firing activities with memristors.This study proposes a switchable memristor to simulate autapse in the Hindmarsh-Rose (HR) neuron model, and introduces a flux-controlled memristor to model the effect of electromagnetic radiation. The proposed 4D HR neuron model without equilibrium points exhibits complex hidden firing activities, which are analyzed through phase diagrams, time series, bifurcation diagrams, Lyapunov exponent spectrums, and two-parameter dynamical maps. The memory attributes of the memristive autapse play a crucial role in the firing activities of the neuron, enabling transitions between periodic spiking with different frequencies and chaotic firing. Additionally, the transition between periodic and chaotic firing induced by the initial value of the switchable memristor is also discovered when it is configured as three different types of memristors. A neuron circuit is designed with current-mode devices to improve accuracy and reduce power consumption. Multisim simulation results are provided to validate the correctness of the neuron model and the effectiveness of numerical analysis. The switchable memristor can exhibit three different memory attributes by controlling the parameter m: nonvolatile discrete memory (m=1), nonvolatile continuum memory (m=0.5), and volatile memory (m=0.25). The study reveals that the firing patterns of the neuron are significantly influenced by the memory attributes of the memristive autapse, and the neuron exhibits different firing patterns when the switchable memristor is configured as different memory states. The results demonstrate that the neuron is sensitive to the initial conditions of the memristive autapse, and the firing patterns can transition without system parameters. The proposed model and circuit design provide a new approach for simulating neuronal firing activities with memristors.