Related papers: Theta neuron subject to delayed feedback: a protot…
We study rotating waves in the Theta model for a ring of synaptically-interacting neurons. We prove that when the neurons are oscillatory, at least one rotating wave always exists. In the case of excitable neurons, we prove that no…
Neural field equations are integro-differential systems describing the macroscopic activity of spatially extended pieces of cortex. In such cortical assemblies, the propagation of information and the transmission machinery induce…
A novel approach to moment closure problem is used to derive low dimensional laws for the dynamics of the moments of the membrane potential distribution in a population of spiking neurons. Using spectral expansion of the density equation we…
We consider generic differential equations in $\mathbb{R}$ with a finite number of hyperbolic equilibria, which are subject to $\omega$--periodic instantaneous perturbative pulses ($\omega>0$). Using the time-$ \omega$ map of the original…
A delayed feedback control framework for stabilizing unstable periodic orbits of linear periodic time-varying systems is proposed. In this framework, act-and-wait approach is utilized for switching a delayed feedback controller on and off…
The stochastic Hodgkin-Huxley neurons considered in this paper replace time-constant deterministic input $a dt$ of the classical deterministic model by increments $\vartheta dt + dX_t$ of a stochastic process: $X$ is Ornstein-Uhlenbeck with…
Sustained rhythmic oscillations, pulsing dynamics, emerge spontaneously when the local connection scheme is randomised in 3-value cellular automata that feature"glider" dynamics. Time-plots of pulsing measures maintain a distinct waveform…
We study the stability of unstable steady states in scalar retarded time-delayed systems subjected to a variable-delay feedback control. The important aspect of such a control problem is that time-delayed systems are already…
We study a network model of two conductance-based pacemaker neurons of differing natural frequency, coupled with either mutual excitation or inhibition, and receiving shared random inhibitory synaptic input. The networks may phase-lock…
Recently discovered constituents of the brain waves -- the oscillons -- provide high-resolution representation of the extracellular field dynamics. Here we study the most robust, highest-amplitude oscillons that manifest in actively…
We consider a system consisting of two delay differential equations with a large parameter, modeling the association of a pair of neurooscillators. The unknown functions describe the changes in the normalized membrane potentials of neurons…
In the present article we show that the energy spectrum of the one-dimensional Dirac equation, in the presence of an attractive vectorial delta potential, exhibits a resonant behavior when one includes an asymptotically spatially vanishing…
We analyze the vibrational resonance in the Duffing oscillator system in the presence of (i) a gamma distributed time-delayed feedback and (ii) integrative time-delayed (uniformly distributed time delays over a finite interval) feedback.…
We study the problem of determining self-sustained oscillations in discrete-time linear time-invariant relay feedback systems. Concretely, we are interested in predicting when such a system admits unimodal oscillations, i.e., when the…
Consistency and predictability of brain functionalities depend on reproducible activity of a single neuron. We identify a reproducible non-chaotic neuronal phase where deviations between concave response latency profiles of a single neuron…
We explore theoretically the navigation of an active particle based on delayed feedback control. The delayed feedback enters in our expression for the particle orientation which, for an active particle, determines (up to noise) the…
We show that Pyragas delayed feedback control can stabilize an unstable periodic orbit (UPO) that arises from a generic subcritical Hopf bifurcation of a stable equilibrium in an n-dimensional dynamical system. This extends results of…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
Working memory requires the brain to maintain information from the recent past to guide ongoing behavior. Neurons can contribute to this capacity by slowly integrating their inputs over time, creating persistent activity that outlasts the…
We establish several delay-independent criteria for the existence and stability of positive periodic solutions of n-dimensional nonautonomous functional differential equation by several fixed point theorems. Examples from positive and…