Physica D: Nonlinear Phenomena ( IF 4 ) Pub Date : 2021-01-23 , DOI: 10.1016/j.physd.2021.132848 Jianhe Shen , Xiang Zhang
For a coupled FitzHugh–Nagumo (FHN) equation with a parameter , when the existence of traveling pulses of this equation was proved in 2013 by Holzer, Doelman and Kaper. Here we adopt a new approach to obtain the existence of the traveling pulse of the same equation for , which includes the degenerate case , where the origin on the critical set loses normal hyperbolicity while it is for . Also we show that the pulse does not exhibit an oscillatory tail at the homoclinic orbit when the time , whereas the classical FHN equation could have an oscillatory tail of the traveling pulse depending on the choice of the parameters of the system. Finally we present an explanation on why traveling pulses cannot exist when .
中文翻译:
FitzHugh-Nagumo耦合方程中的行进脉冲
对于带有参数的耦合FitzHugh–Nagumo(FHN)方程 , 什么时候 Holzer,Doelman和Kaper于2013年证明了该方程行进脉冲的存在。在这里,我们采用一种新的方法来获得存在相同方程的行进脉冲,其中包括简并的案例 ,其中关键集合的原点在 。我们还表明,当时间为零时,脉冲在同斜轨道上没有振荡尾,而经典FHN方程可能会根据系统参数的选择而产生行进脉冲的振荡尾部。最后,我们解释了为什么当。