Influence of external current and noise on modes of electrical activities and energy of Hindmarsh-Rose model coupled by memristive synapses

The progress of medicine and biological have lengthen life, thus increasing the incidence of degenerative illnesses such as Parkinson, Alzheimer. To help patients suffering from those illnesses, we can use a therapy technique which consists to deliver within a precise region of the central nervous system an electrical signal in order to regulate unnatural impulses. That therapeutic method, since it requires surgical procedure is only needed when medication stops to have effect on the patients. In this work, we study the effects of periodic external current and noise on the modes of electrical activities; Furthermore we estimate the energy of a 2D Hindmarsh-Rose coupled by memristive synapses. Results show that the neuronal network exhibits bursting regime in the presence of periodic external force and noise. Noises make those bursts irregular over time evolution. Concerning the energy analysis, we observe an increase of the energy when the amplitude of the external force increases. Lastly, we show that noise makes the energy of the neuronal network to oscillate with different amplitudes. Large amplitude is observed in the presence of large values of the amplitude of the noise.