2024/08/06 by M. Al-Amin, M. Nurul Islam, M. Ali Akbar
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #stochastic dynamics and bifurcation #Chaos control and synchronization
paper · doi:10.1142/s0217984924504827
The nonlinear Fitzhugh–Nagumo (FN) model is a well-known nonlinear reaction-diffusion model, which is a simplified form of the Hodgkin–Huxley (HH) model. Several important phenomena are analyzed via the FN model, such as nerve impulse transmission through the neurons, biological population genetics, noise formations in circuit theory, intercellular trigger wave propagation, and others. The FN model is definitely an important mathematical model in the domain of neurobiological sciences and engineering applications. In this paper, we study the nonlinear fractional FN model, computationally and numerically using the auxiliary equation (AE) method through the conformable derivative. We have established numerous fresh, useful, efficient and wide-ranging closed-form traveling wave solutions of the model. Additionally, we examine the influence of fractional parameter on the signal transmission through the nerve system and other related wave propagation by sketching the three-dimensional graphs of the solutions with the aid of the Mathematica program. The established results authenticate the efficiency and reliability of the considered method.