6533b856fe1ef96bd12b2470
RESEARCH PRODUCT
Heteroclinic contours and self-replicated solitary waves in a reaction–diffusion lattice with complex threshold excitation
D. S. ShapinStéphane BinczakA. S. DmitrichevV. B. KazantsevJean-marie BilbaultVladimir I. Nekorkinsubject
Classical mechanicsPhase spaceReaction–diffusion systemComplex systemPattern formationHeteroclinic cycleStatistical and Nonlinear PhysicsHeteroclinic orbitHomoclinic orbitHeteroclinic bifurcationCondensed Matter PhysicsMathematicsdescription
Abstract The space–time dynamics of the network system modeling collective behavior of electrically coupled nonlinear cells is investigated. The dynamics of a local cell is described by the FitzHugh–Nagumo system with complex threshold excitation. Heteroclinic orbits defining traveling wave front solutions are investigated in a moving frame system. A heteroclinic contour formed by separatrix manifolds of two saddle-foci is found in the phase space. The existence of such structure indicates the appearance of complex wave patterns in the network. Such solutions have been confirmed and analyzed numerically. Complex homoclinic orbits found in the neighborhood of the heteroclinic contour define the propagation of composite pulse excitations that can be self-replicated in collisions leading to the appearance of complex wave patterns.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-10-01 | Physica D: Nonlinear Phenomena |