title: Oscillatory pulses and wave trains in a bistable reaction-diffusion system with cross diffusion.
abstract: We study waves with exponentially decaying oscillatory tails in a reaction-diffusion system with linear cross diffusion. To be specific, we consider a piecewise linear approximation of the FitzHugh-Nagumo model, also known as the Bonhoeffer-van der Pol model. We focus on two types of traveling waves, namely solitary pulses that correspond to a homoclinic solution, and sequences of pulses or wave trains, i.e., a periodic solution. The effect of cross diffusion on wave profiles and speed of propagation is analyzed. We find the intriguing result that both pulses and wave trains occur in the bistable cross-diffusive FitzHugh-Nagumo system, whereas only fronts exist in the standard bistable system without cross diffusion.
authors.affiliation: Federal Research Center for Computer Science and Control, Russian Academy of Sciences, Vavilova 40, 119333 Moscow, Russia.
authors.forename: Evgeny P
authors.initials: EP
authors.lastname: Zemskov
authors.affiliation: Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Institutskaya 3, 142290 Pushchino, Moscow Region, Russia.
authors.forename: Mikhail A
authors.initials: MA
authors.lastname: Tsyganov
authors.affiliation: Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, USA.
authors.forename: Werner
authors.initials: W
authors.lastname: Horsthemke