Abstract
We explore and analyze the nonlinear switching dynamics of neuronal networks with non-homogeneous connectivity. The general significance of such transient dynamics for brain function is unclear; however, for instance decision-making processes in perception and cognition have been implicated with it. The network under study here is comprised of three subnetworks of either excitatory or inhibitory leaky integrate-and-fire neurons, of which two are of the same type. The synaptic weights are arranged to establish and maintain a balance between excitation and inhibition in case of a constant external drive. Each subnetwork is randomly connected, where all neurons belonging to a particular population have the same in-degree and the same out-degree. Neurons in different subnetworks are also randomly connected with the same probability; however, depending on the type of the pre-synaptic neuron, the synaptic weight is scaled by a factor. We observed that for a certain range of the “within” versus “between” connection weights (bifurcation parameter), the network activation spontaneously switches between the two sub-networks of the same type. This kind of dynamics has been termed “winnerless competition”, which also has a random component here. In our model, this phenomenon is well described by a set of coupled stochastic differential equations of Lotka-Volterra type that imply a competition between the subnetworks. The associated mean-field model shows the same dynamical behavior as observed in simulations of large networks comprising thousands of spiking neurons. The deterministic phase portrait is characterized by two attractors and a saddle node, its stochastic component is essentially given by the multiplicative inherent noise of the system. We find that the dwell time distribution of the active states is exponential, indicating that the noise drives the system randomly from one attractor to the other. A similar model for a larger number of populations might suggest a general approach to study the dynamics of interacting populations of spiking networks.
Highlights
Animal behavior emerges as a consequence of neuronal interactions and their plastic changes during learning
When we consider a typical system in the switching regime, the parameters for the scenario with two excitatory one inhibitory population (EEI) are J = 0.1 mV and w = 2.5 and the parameters for the scenario with one excitatory and two-inhibitory populations are J = 0.1 mV and w = 0.7
The nonlinearities governing the dynamics of the system, which are inferred from simulation results, as well as predictions from the corresponding Lotka-Volterra model will be demonstrated
Summary
Animal behavior emerges as a consequence of neuronal interactions and their plastic changes during learning. Self-organization through plasticity is what makes neuronal networks capable. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Synaptic Activity as a Switch Between Dynamical States in a Network. Fast global oscillations in networks of integrate-and-fire neurons with low firing rates.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
