303 citations · 369 across the 5 of their papers we have counts for
9 papers
Sensitivity to control signals in triphasic rhythmic neural systems: a comparative mechanistic analysis via infinitesimal local timing response curves
Zhuojun Yu, Jonathan E. Rubin, Peter J. Thomas
Similar activity patterns may arise from model neural networks with distinct coupling properties and individual unit dynamics. These similar patterns may, however, respond differen…
Dynamics of ramping bursts in a respiratory neuron model
Muhammad U. Abdulla, Ryan S. Phillips, Jonathan E. Rubin
Intensive computational and theoretical work has led to the development of mutliple mathematical models for bursting in respiratory neurons in the pre-Bötzinger Complex (pre-BötC)…
Type III Responses to Transient Inputs in Hybrid Nonlinear Neuron Models
Jonathan Rubin, Justyna Signerska-Rynkowska, Jonathan D. Touboul
Experimental characterization of neuronal dynamics involves recording both of spontaneous activity patterns and of responses to transient and sustained inputs. While much theoretic…
Interactions of Solitary Pulses of E. coli in a One-Dimensional Nutrient Gradient
Glenn Young, Mahmut Demir, Hanna Salman +2
We study an anomalous behavior observed in interacting E. coli populations. When two populations of E. coli are placed on opposite ends of a long channel with a supply of nutrient…
Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike adding and chaos
Jonathan E. Rubin, Justyna Signerska-Rynkowska, Jonathan D. Touboul +1
In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and…
Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations
Jonathan E. Rubin, Justyna Signerska-Rynkowska, Jonathan Touboul +1
This work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation a…
Traveling Wave Solutions in a Chain of periodically Forced Couple Nonlinear Oscillators
Mei Duanmu, Nathaniel Whitaker, Panos Kevrekidis +2
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillato…
Equilibrium Properties of Temporally Asymmetric Hebbian Plasticity
Jonathan Rubin, Daniel D. Lee, H. Sompolinsky
A theory of temporally asymmetric Hebb (TAH) rules which depress or potentiate synapses depending upon whether the postsynaptic cell fires before or after the presynaptic one is pr…
Existence and stability of hole solutions to complex Ginzburg-Landau equations
Todd Kapitula, Jonathan Rubin
We consider the existence and stability of the hole, or dark soliton, solution to a Ginzburg-Landau perturbation of the defocusing nonlinear Schroedinger equation (NLS), and to the…