Analyzing neuronal networks using discrete-time dynamics

Analyzing Neuronal Networks Using Discrete-Time Dynamics.

We develop mathematical techniques for analyzing detailed Hodgkin-Huxley like models for excitatory-inhibitory neuronal networks. Our strategy for studying a given network is to first reduce it to a discrete-time dynamical system. The discrete model is considerably easier to analyze, both mathematically and computationally, and parameters in the discrete model correspond directly to parameters ...

Reducing Neuronal Networks to Discrete Dynamics.

We consider a general class of purely inhibitory and excitatory-inhibitory neuronal networks, with a general class of network architectures, and characterize the complex firing patterns that emerge. Our strategy for studying these networks is to first reduce them to a discrete model. In the discrete model, each neuron is represented as a finite number of states and there are rules for how a neu...

Dynamics of a discrete-time plant-herbivore model

Dynamics for Discrete-Time Cellular Neural Networks

This presentation investigates the dynamics of discrete-time cellular neural networks (DT-CNN). In contrast to classical neural networks that are mostly gradient-like systems, DT-CNN possesses both complete stability and chaotic behaviors as different parameters are considered. An energylike function which decreases along orbits of DT-CNN as well as the existence of a globally attracting set ar...

Digraphs vs. Dynamics in Discrete Models of Neuronal Networks

It has recently been shown that discrete-time finite-state models can reliably reproduce the ordinary differential equation (ODE) dynamics of certain neuronal networks. We study which dynamics are possible in these discrete models for certain types of network connectivities. In particular we are interested in the number of different attractors and bounds on the lengths of attractors and transie...