Related papers: Comparison principles and asymptotic behavior of d…
The concept of temporal networks provides a framework to understand how the interaction between system components changes over time. In empirical communication data, we often detect non-Poissonian, so-called bursty behavior in the activity…
In this paper, we investigate the convergence of asymptotic systems in non-autonomous Cohen--Grossberg neural network models, which include both infinite discrete time-varying and distributed delays. We derive stability results under…
Closed-loop neurotechnology requires the capability to predict the state evolution and its regulation under (possibly) partial measurements. There is evidence that neurophysiological dynamics can be modeled by fractional-order dynamical…
Cycles of word usage have been described using an integro-differential Volterra model close to a Hopf bifurcation. Here we transform this system to a phase model, which allows us to phase-couple the words and address the observation of…
Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions…
We investigate the dynamics of a network consisting of an array of identical cortical units with nearest neighbor interactions under periodic arousal. Each unit consists of two interconnected populations of neurons tuned to a state in which…
Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…
Complexity in the temporal organization of neural systems may be a reflection of the diversity of its neural constituents. These constituents, excitatory and inhibitory neurons, comprise an invariant ratio in vivo and form the substrate for…
We study a Cucker-Smale-type flocking model with distributed time delay where individuals interact with each other through normalized communication weights. Based on a Lyapunov functional approach, we provide sufficient conditions for the…
Dormancy is a widespread adaptive strategy that enables populations to persist in fluctuating environments, yet how its benefits depend on the temporal structure of environmental variability remains unclear. We examine how dormancy…
The pairwise maximum entropy model, also known as the Ising model, has been widely used to analyze the collective activity of neurons. However, controversy persists in the literature about seemingly inconsistent findings, whose significance…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical…
Slowly driven dissipative systems may evolve to a critical state where long periods of apparent equilibrium are punctuated by intermittent avalanches of activity. We present a self-organized critical model of punctuated equilibrium behavior…
This article proposes methods to model nonstationary temporal graph processes. This corresponds to modelling the observation of edge variables (relationships between objects) indicating interactions between pairs of nodes (or objects)…
Diabetic neuropathy is a disorder characterized by impaired nerve function and reduction of the number of epidermal nerve fibers per epidermal surface. Additionally, as neuropathy related nerve fiber loss and regrowth progresses over time,…
The approach to equilibrium is studied for long-range quantum Ising models where the interaction strength decays like r^{-\alpha} at large distances r with an exponent $\alpha$ not exceeding the lattice dimension. For a large class of…
Many mathematical models of interacting agents assume that individual interactions scale down in proportion to the network size, ensuring that the combined input received from the network does not diverge. In theoretical neuroscience,…
We study two delay-coupled FitzHugh-Nagumo systems, introducing a mismatch between the delay times, as the simplest representation of interacting neurons. We demonstrate that the presence of delays can cause periodic oscillations which…
Many questions in neuroscience involve understanding of the responses of large populations of neurons. However, when dealing with large-scale neural activity, interpretation becomes difficult, and comparisons between two animals, or across…