Abstract
Nonlinear excitations of waves are investigated in a two-dimensional cell network with bidirectional paracrine signaling, both in the longitudinal and transversal directions. The semi-discrete approximation is used to show that the dynamics of the intercellular
waves can be reduced to complex Ginzburg–Landau equations, depending on the high- or low-frequency regime. The onset of modulational instability is addressed, where the instability features of the low- and high-frequency modes are compared via the instability growth rate. The
-expansion method is employed to find analytically spiral-like wave solutions for the two dynamical regimes. Their response to the effect of paracrine coupling is also addressed.
Disclosure statement
No potential conflict of interest was reported by the authors.