6533b83afe1ef96bd12a719b

RESEARCH PRODUCT

Pattern selection in the 2D FitzHugh–Nagumo model

Marco SammartinoGaetana GambinoMaria Carmela LombardoG. Rubino

subject

PhysicsTuring instabilityApplied MathematicsGeneral MathematicsNumerical analysis010102 general mathematicsMathematical analysisSquare pattern01 natural sciencesSquare (algebra)010305 fluids & plasmasFitzHugh–Nagumo modelNonlinear systemAmplitudeBounded function0103 physical sciencesAmplitude equationMathematics (all)FitzHugh–Nagumo model0101 mathematicsEigenvalues and eigenvectorsBifurcation

description

We construct square and target patterns solutions of the FitzHugh–Nagumo reaction–diffusion system on planar bounded domains. We study the existence and stability of stationary square and super-square patterns by performing a close to equilibrium asymptotic weakly nonlinear expansion: the emergence of these patterns is shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue without resonance. The system is also shown to support the formation of axisymmetric target patterns whose amplitude equation is derived close to the bifurcation threshold. We present several numerical simulations validating the theoretical results.

yearjournalcountryeditionlanguage
2018-09-29Ricerche di Matematica
https://doi.org/10.1007/s11587-018-0424-6