A survey on the modeling of hybrid behaviors: How to account for impulsive jumps properly
We propose an overview of the modeling approaches for the mathematical description and
analysis of processes that combine continuous and discontinuous behavior, namely …
analysis of processes that combine continuous and discontinuous behavior, namely …
Pulse-timing symmetry breaking in an excitable optical system with delay
Excitable systems with delayed feedback are important in areas from biology to
neuroscience and optics. They sustain multistable pulsing regimes with different numbers of …
neuroscience and optics. They sustain multistable pulsing regimes with different numbers of …
On the interpretation of Dirac δ pulses in differential equations for phase oscillators
In this note, we discuss the usage of the Dirac δ function in models of phase oscillators with
pulsatile inputs. Many authors use a product of the delta function and the phase response …
pulsatile inputs. Many authors use a product of the delta function and the phase response …
Embedding the dynamics of a single delay system into a feed-forward ring
We investigate the relation between the dynamics of a single oscillator with delayed self-
feedback and a feed-forward ring of such oscillators, where each unit is coupled to its next …
feedback and a feed-forward ring of such oscillators, where each unit is coupled to its next …
Noise-induced switching in an oscillator with pulse delayed feedback: A discrete stochastic modeling approach
VV Klinshov, O D'Huys - Chaos: An Interdisciplinary Journal of …, 2022 - pubs.aip.org
We study the dynamics of an oscillatory system with pulse delayed feedback and noise of
two types:(i) phase noise acting on the oscillator and (ii) stochastic fluctuations of the …
two types:(i) phase noise acting on the oscillator and (ii) stochastic fluctuations of the …
Desynchronization by phase slip patterns in networks of pulse-coupled oscillators with delays: Desynchronization by phase slip patterns
Coupling delays may cause drastic changes in the dynamics of oscillatory networks. In the
present paper we investigate how coupling delays alter synchronization processes in …
present paper we investigate how coupling delays alter synchronization processes in …
Adaptive myelination causes slow oscillations in recurrent neural loops
VV Klinshov, VI Nekorkin - Chaos: An Interdisciplinary Journal of …, 2024 - pubs.aip.org
The brain is known to be plastic, ie, capable of changing and reorganizing as it develops
and accumulates experience. Recently, a novel form of brain plasticity was described which …
and accumulates experience. Recently, a novel form of brain plasticity was described which …
Existence and stability criteria for global synchrony and for synchrony in two alternating clusters of pulse-coupled oscillators updated to include conduction delays
AV Srinivas, CC Canavier - Mathematical Biosciences, 2024 - Elsevier
Abstract Phase Response Curves (PRCs) have been useful in determining and analyzing
various phase-locking modes in networks of oscillators under pulse-coupling assumptions …
various phase-locking modes in networks of oscillators under pulse-coupling assumptions …
Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing
CR Laing, B Krauskopf - Proceedings of the Royal …, 2022 - royalsocietypublishing.org
We consider a single theta neuron with delayed self-feedback in the form of a Dirac delta
function in time. Because the dynamics of a theta neuron on its own can be solved explicitly …
function in time. Because the dynamics of a theta neuron on its own can be solved explicitly …
Jittering waves in rings of pulse oscillators
Rings of oscillators with delayed pulse coupling are studied analytically, numerically, and
experimentally. The basic regimes observed in such rings are rotating waves with constant …
experimentally. The basic regimes observed in such rings are rotating waves with constant …