Reliability and energy function of an oscillator and map neuron

Area of Science:

• Neuroscience
• Computational Neuroscience
• Biophysics

Background:

• Neurons process external stimuli via electrical activity.
• Oscillator and map neuron models exhibit similar responses, but mechanisms remain unclear.
• Membrane properties and channel function influence neuronal dynamics.

Purpose of the Study:

• To propose a theoretical neuron model incorporating membrane properties and a memristive channel.
• To investigate the influence of temperature on neuronal dynamics.
• To analyze the behavior of an equivalent map neuron derived from the oscillator model.

Main Methods:

• Developed a theoretical neuron model with two capacitive variables and a temperature-dependent, electric-field-sensitive memristive channel.
• Implemented a circuit approach with capacitors, a thermistor, and a charge-dependent memristor (CDM).
• Applied linear transformation to oscillator neuron variables to derive an equivalent map neuron.

Main Results:

• The temperature-dependent and memristive neuron model is described by a four-variable nonlinear oscillator with a defined energy function.
• An equivalent map neuron was obtained for dynamical analysis, energy definition, and adaptive control.
• Coherence resonance was detected under noisy excitation, demonstrating model robustness.

Conclusions:

• The study provides a method to obtain reliable map neurons with precise energy functions.
• The proposed model facilitates reasonable adaptive control laws based on energy flow.
• This work advances the understanding of neuronal dynamics influenced by physical properties.