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Leap-frog patterns in systems of two coupled FitzHugh-Nagumo units
We study a system of two identical FitzHugh-Nagumo units with a mutual
linear coupling in the fast variables. While an attractive coupling always
leads to synchronous behavior, a repulsive coupling can give rise to
dynamical regimes with alternating spiking order, called leap-frogging. We
analyze various types of periodic and chaotic leap-frogging regimes, using
numerical pathfollowing methods to investigate their emergence and stability,
as well as to obtain the complex bifurcation scenario which organizes their
appearance in parameter space. In particular, we show that the stability
region of the simplest periodic leap-frog pattern has the shape of a locking
cone pointing to the canard transition of the uncoupled system. We also
discuss the role of the timescale separation in the coupled FitzHugh-Nagumo
system and the relation of the leap-frog solutions to the theory of
mixed-mode oscillations in multiple timescale systems