Related papers: Theta neuron subject to delayed feedback: a protot…
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…
Almost all organisms show some kind of time periodicity in their behavior. Especially in mammals the neurons of the suprachiasmatic nucleus form a biological clock regulating the activity-inactivity cycle of the animal. This clock is…
In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show…
The plasticity of the conduction delay between neurons plays a fundamental role in learning. However, the exact underlying mechanisms in the brain for this modulation is still an open problem. Understanding the precise adjustment of…
We prove an analytical limitation on the use of time-delayed feedback control for the stabilization of periodic orbits in autonomous systems. This limitation depends on the number of real Floquet multipliers larger than unity, and is…
This paper presents a control-oriented delay-based modeling approach for the exponential stabilization of a scalar neutral functional differential equation, which is then applied to the local exponential stabilization of a one-layer neural…
Excitability, encountered in numerous fields from biology to neurosciences and optics, is a general phenomenon characterized by an all-or-none response of a system to an external perturbation. When subject to delayed feedback, excitable…
We show that \emph{stochastic bursting} is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation,…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
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…
We analyse the stochastic dynamics of a bistable system under the influence of time-delayed feedback. Assuming an asymmetric potential, we show the existence of a regime in which the systems dynamic displays excitability by calculating the…
Animals move smoothly and reliably in unpredictable environments. Models of sensorimotor control have assumed that sensory information from the environment leads to actions, which then act back on the environment, creating a single,…
Many systems are modulated by unknown slow processes. This hinders analysis in highly non-linear systems, such as excitable systems. We show that for such systems, if the input matches the sparse `spiky' nature of the output, the spiking…
Two identical autonomous dynamical systems coupled in a master-slave configuration can exhibit anticipated synchronization (AS) if the slave also receives a delayed negative self-feedback. Recently, AS was shown to occur in systems of…
Time-delayed feedback control, attributed to Pyragas (1992 Physics Letters 170(6) 421-428), is a method known to stabilise periodic orbits in low dimensional chaotic dynamical systems. A system of the form…
Stochastic resetting has shown promise in enhancing the stability of dynamical systems. Here, we apply this concept to theta neuron networks with partial resetting, where only a fraction of neurons is intermittently reset. We examine both…
We propose a paradigmatic model system, a subcritical Hopf normal form subjected to noise and time-delayed feedback, to investigate the impact of time delay on coherence resonance in non-excitable systems. We develop analytical tools to…
We consider a ring network of quadratic integrate-and-fire neurons with nonlocal synaptic and gap junction coupling. The corresponding neural field model supports solutions such as standing and travelling waves, and also lurching waves. We…
The theoretical analysis and numerical simulations of the magnetron operation with a feedback loop were performed assuming that the delay of the electromagnetic wave propagating in the loop is constant whereas the phase of the complex…
In this paper, a kind of neural network with time-varying delays is proposed to solve the problems of quadratic programming. The delay term of the neural network changes with time t. The number of neurons in the neural network is n + h, so…