25 citations · 29 across the 7 of their papers we have counts for
7 papers
Deviations from global coupling in adaptive oscillator networks: a mean-field theory for the variance of coupling weights
Richard Gast, Shotaro Takasu, Juergen Kurths +1
A wide range of physical and biological systems are adaptive networks, in which the dynamics of the nodes and of the edges connecting them co-evolve. Mean-field reductions of such…
Local connectivity balance shapes population dynamics in random recurrent networks
Shotaro Takasu, Richard Gast, Ann Kennedy
Disordered dynamical systems comprising many interacting units, from ecological communities to neural circuits, are ubiquitous, and understanding how connectivity shapes their coll…
A multi-ensemble mean-field reduction method for networks of globally coupled phase oscillators with arbitrary parameter distributions
Richard Gast, Shotaro Takasu, Helmut Schmidt +1
Understanding the dynamical properties of coupled phase oscillator systems with heterogeneous oscillator frequencies has been a long-standing challenge of complex systems theory. W…
PyRates -- A Code-Generation Tool for Dynamical Systems Modeling
Richard Gast, Thomas R. Knösche, Ann Kennedy
Mathematical models allow us to gain a deeper understanding of real-world dynamical systems. One of the most powerful mathematical frameworks for modeling real-world phenomena are…
Macroscopic Dynamics of Neural Networks with Heterogeneous Spiking Thresholds
Richard Gast, Sara A. Solla, Ann Kennedy
Mean-field theory links the physiological properties of individual neurons to the emergent dynamics of neural population activity. These models provide an essential tool for studyi…
Effects of Neural Heterogeneity on Spiking Neural Network Dynamics
Richard Gast, Sara A. Solla, Ann Kennedy
The brain is composed of complex networks of interacting neurons that express considerable heterogeneity in their physiology and spiking characteristics. How does neural heterogene…
Mean-field approximations of networks of spiking neurons with short-term synaptic plasticity
Richard Gast, Thomas R. Knösche, Helmut Schmidt
Low-dimensional descriptions of neural network dynamics are an effective tool for bridging different scales of organization of brain structure and function. Recent advances in deri…