Since the neurologists Hindmarsh and Rose improved the Hodgkin-Huxley model to provide a better understanding on the diversity of neural response, features like pole of attraction unfolding complex bifurcation for the membrane potential was still a mystery. This work explores the possible existence of chaotic poles of attraction in the dynamics of Hindmarsh-Rose neurons with an external current input. Combining with fractional differentiation, the model is generalized with the introduction of an additional parameter, the non-integer order of the derivative σ , and solved numerically thanks to the Haar Wavelets. Numerical simulations of the membrane potential dynamics show that in the standard case where the control parameter σ = 1, the nerve cell’s behavior seems irregular with a pole of attraction generating a limit cycle. This irregularity accentuates as σ decreases (σ = 0.9 and σ = 0.85) with the pole of attraction becoming chaotic.
|Number of pages||9|
|Journal||Chaos (Woodbury, N.Y.)|
|Publication status||Published - 2019|