Analytical and numerical solutions of the <scp>Fitzhugh–Nagumo</scp> equation and their multistability behavior
Bilge İnan, Khalid K. Ali, Asit Saha, Turgut Ak
Abstract
Abstract In this paper, we propose an analytical method and a modification of explicit exponential finite difference method (EEFDM) for analytical and numerical solutions of the Fitzhugh–Nagumo (FN) and Newell–Whitehead (NW) equations. The method is improved computationally by using the Padé approximation technique. Furthermore, multistability behavior of traveling wave solutions of the FN and NW equations are examined in presence of external forcing. It is observed that there exist coexisting periodic and quasiperiodic orbits for the FN equation, where as only quasiperiodic orbits is observed in case of NW equation.
Topics & Concepts
Quasiperiodic functionMultistabilityMathematicsForcing (mathematics)Mathematical analysisTraveling waveExponential functionApplied mathematicsPhysicsQuantum mechanicsNonlinear systemNonlinear Waves and SolitonsQuantum chaos and dynamical systemsAdvanced Differential Equations and Dynamical Systems