Related papers: Directional excitability in Hilbert spaces
Willems' fundamental lemma asserts that all trajectories of a linear time-invariant system can be obtained from a finite number of measured ones, assuming that controllability and a persistency of excitation condition hold. We show that…
Chimera is a fascinating phenomenon of coexisting synchronized and desynchronized behaviour that was discovered in networks of nonlocally coupled identical phase oscillators over ten years ago. Since then, chimeras were found in numerous…
We examine the effects of stochastic input currents on the firing behavior of two excitable neurons coupled with fast excitatory synapses. In such cells (models), typified by the quadratic integrate and fire model, mutual synaptic coupling…
We study a lattice model where the coupling stochastically switches between repulsive (subtractive) and attractive (additive) at each site with probability p at every time instance. We observe that such kind of coupling stabilizes the local…
Fluidic iontronics is emerging as a distinctive platform for implementing neuromorphic circuits, characterized by its reliance on the same aqueous medium and ionic signal carriers as the brain. Drawing upon recent theoretical advancements…
In the last century, most sensorimotor studies of cortical neurons relied on average firing rates. Rate coding is efficient for fast sensorimotor processing that occurs within a few seconds. Much less is known about the neural mechanisms…
We study the emergence of many-body correlations in the stationary state of continuously-driven, strongly-interacting dissipative system. Specifically, we examine resonant optical excitations of Rydberg states of atoms interacting via…
We experimentally demonstrate that networks of identical photonic spiking neurons based on coupled degenerate parametric oscillators can show various chimera states, in which, depending on their local synchronization and desynchronization,…
Analytical expressions are put forward to investigate the forced spiking activity of abstract neuron models such as the driven leaky integrate-and-fire (LIF) model. The method is valid in a wide parameter regime beyond the restraining…
We develop a theory for the emergence of global firings in non-identical excitable systems subject to noise. Three different dynamical regimes arise: sub-threshold motion, where all elements remain confined near the fixed point; coherent…
Experiments show that spike-triggered stimulation performed with Bidirectional Brain-Computer-Interfaces (BBCI) can artificially strengthen connections between separate neural sites in motor cortex (MC). What are the neuronal mechanisms…
We consider third-order dynamic systems which have an integral feedback action and discontinuous relay disturbance. More specifically for the applications, the focus is on the integral plus state-feedback control of the motion systems with…
Exploiting the rich phenomenology of periodically-driven many-body systems is notoriously hindered by persistent heating in both the classical and quantum realm. Here, we investigate to what extent coupling to a large thermal reservoir…
We introduce a nonlinear modification of the classical Hawkes process, which allows inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model for…
Firing rate models are dynamical systems widely used in applied and theoretical neuroscience to describe local cortical dynamics in neuronal populations. By providing a macroscopic perspective of neuronal activity, these models are…
We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky…
Numerical simulations of classical pattern forming reaction-diffusion systems indicate that they often operate in the strongly nonlinear regime, with the final steady-state consisting of a spatially repeating pattern of localized spikes. In…
Contemporary modeling approaches to the dynamics of neural networks consider two main classes of models: biologically grounded spiking neurons and functionally inspired rate-based units. The unified simulation framework presented here…
In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…
We study the dynamics of up to two Rydberg excitations and the correlation growth in a chain of atoms coupled to a photonic crystal waveguide. In this setup, an excitation can hop from one atom to another via exponentially decaying exchange…