Bifurcation Analysis and Solitary Wave Analysis of the Nonlinear Fractional Soliton Neuron Model

Abstract

Fractional nonlinear soliton neuron model (FNLSNM) equation is mathematical interpretations employed to describe a wide range of complicated phenomena occurring in neuroscience and obscure mode of action of numerous anesthetics. FNLSNM equation explains how action potential is started and performed along axons depending on a thermodynamic theory of nerve pulse propagation. The signals that pass through the cell membrane were suggested to be in different forms of solitary sound pulses which can be modeled as solitons. So, the scientific community has exposed momentous interest in FNLSNM equation and their Bifurcation analysis (BA) and solitary wave analysis (SWA). This study employs the modified $\left( {\frac{G^{\prime}}{G}} \right)$-expansion (M-$\left( {\frac{G^{\prime}}{G}} \right)$-E) method to derive BA and SWA for the FNLSNM equation, utilizing the Jumarie’s fractional derivative (JFD). 3D and BA figures are presented of FNLSNM equation. Furthermore, 2D plots are produced to examine how the fractional parameter (FP) and time space parameter (TSP) affects the SWA. The Hamiltonian function (HF) is established to advance analyses the dynamics of the phase plane (PP). The simulations were performed through Python and MAPLE software instruments. The effects of different studies showed that the M-$\left( {\frac{G^{\prime}}{G}} \right)$-E method is pretty well-organized and is well well-matched for the difficulties arising in neuroscience and mathematical physics.