Enhanced Pulse Propagation in Non-Linear Arrays of Oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (1D) or energy front (2D) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

COMPRESSION OF ENVELOPE SOLITONS IN NONLINEAR ELECTRICAL LINES

La propagation des solitons enveloppe dans les lignes non linéaires de transmission électrique et de transmission Josephson est étudiée sous l'aspect théorique et en simulation numérique. Dans l'approximation des milieux continus et la limite des faibles amplitudes, les équations caractéristiques de ces lignes se ramènent à l'équation NLS . La solution "à deux solitons enveloppe" se propage parfaitement dans les lignes considérées avec des phénoménes de récurrence et de compression d'enveloppe. Ceci est observé également pour des profils d'excitation non solution de NLS, ce qui est d'un grand intérêt pour les applications pratiques.We study theoretically and numerically the properties of envelope solitons in a nonlinear electrical transmission line and in a Josephson transmission line, in a small amplitude limit. In the continuum limit and weak amplitude limit, we reduce the characteristic equations of these systems to NLS equation and we study "the two solitons envelope" solutions which propagate with recurrence phenomena along the two types of lines. Compression of envelope is observed for the academic solutions but we show that, even with a non-academic profile, the full width at half maximum is reduced, which is of a great interest for practical applications

Spiking dynamics of interacting oscillatory neurons

International audienceSpiking sequences emerging from dynamical interaction in a pair of oscillatory neurons are investigated theoretically and experimentally. The model comprises two unidirectionally coupled FitzHugh-Nagumo units with modified excitability (MFHN). The first (master) unit exhibits a periodic spike sequence with a certain frequency. The second (slave) unit is in its excitable mode and responds on the input signal with a complex (chaotic) spike trains. We analyze the dynamic mechanisms underlying different response behavior depending on interaction strength. Spiking phase maps describing the response dynamics are obtained. Complex phase locking and chaotic sequences are investigated. We show how the response spike trains can be effectively controlled by the interaction parameter and discuss the problem of neuronal information encoding