Showing papers by "Steven H. Strogatz published in 1988"
••
TL;DR: In this paper, the authors studied phase-locking in a network of coupled nonlinear oscillators with local interactions and random intrinsic frequencies and derived an exact expression for the probability of phase locking in a linear chain of such oscillators.
178 citations
••
TL;DR: In this article, Love Affairs and Differential Equations (LDA) are used to describe the relationship between differentials and differentials in a set of differentially equational equations.
Abstract: (1988). Love Affairs and Differential Equations. Mathematics Magazine: Vol. 61, No. 1, pp. 35-35.
106 citations
••
TL;DR: In this article, the authors studied mutual synchronisation in a model of interacting limit cycle oscillators with random intrinsic frequencies, and showed rigorously that the model exhibits no long-range order in one dimension, and that in higher-dimensional lattices, large clusters of synchronised oscillators necessarily have a sponge-like structure.
Abstract: The authors study mutual synchronisation in a model of interacting limit cycle oscillators with random intrinsic frequencies. It is shown rigorously that the model exhibits no long-range order in one dimension, and that in higher-dimensional lattices, large clusters of synchronised oscillators necessarily have a sponge-like structure. Surprisingly, the phase-locking behaviour of the mean-field model is completely different from that of any finite-dimensional lattice, indicating that d= infinity is the upper critical dimension for phase locking.
87 citations
••
TL;DR: On presente une analyse de champ moyen d'un systeme dynamique a plusieurs corps qui modelise le transport de l'onde de densite de charge en presence d'impuretes d'ancrage aleatoires.
Abstract: We present a mean-field analysis of a many-body dynamical system which models charge-density-wave transport in the presence of random pinning impurities. Phase slip between charge-density-wave domains is modeled by a coupling term that is periodic in the phase differences. When driven by an external field, the system exhibits a first-order depinning transition, hysteresis, and switching between pinned and sliding states, and a delayed onset of sliding near threshold.
55 citations