<p>This work is dedicated to investigating the splitting expression of solutions for a stochastic FitzHugh–Nagumo type equation with time delay. At first, through the construction of upper and lower solutions for second-order delay differential equations, it is examined that the deterministic FitzHugh–Nagumo type equation with time delay admits the existence of traveling wave front solutions. Then, by means of an appropriate weight function and evaluating low-order fluctuations within the weight function space, the solution of the stochastic FitzHugh–Nagumo type equation with time delay can be decomposed into the sum of a randomly modulated travelling wave and a small remainder term.</p>

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Modulation Analysis for Stochastic FitzHugh–Nagumo Type Equation with Time Delay

  • Yu Liu,
  • Guanggan Chen,
  • Shuyong Li

摘要

This work is dedicated to investigating the splitting expression of solutions for a stochastic FitzHugh–Nagumo type equation with time delay. At first, through the construction of upper and lower solutions for second-order delay differential equations, it is examined that the deterministic FitzHugh–Nagumo type equation with time delay admits the existence of traveling wave front solutions. Then, by means of an appropriate weight function and evaluating low-order fluctuations within the weight function space, the solution of the stochastic FitzHugh–Nagumo type equation with time delay can be decomposed into the sum of a randomly modulated travelling wave and a small remainder term.