On the interpretation of Dirac δ pulses in differential equations for phase oscillators

DOI10.1063/5.0040995zbMath1459.34091arXiv2012.01836OpenAlexW3108695717WikidataQ115327820 ScholiaQ115327820MaRDI QIDQ3388643

Vladimir Klinshov, Leonhard Lücken, P. V. Feketa

Publication date: 6 May 2021

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.01836

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (6)

Strong solutions of a semilinear impulsive pseudoparabolic equation with an infinitesimal initial layer ⋮ Weak solutions of impulsive pseudoparabolic equations with an infinitesimal transition layer ⋮ A survey on the modeling of hybrid behaviors: how to account for impulsive jumps properly ⋮ The impulsive heat equation with the Volterra transition layer ⋮ Strong solutions of impulsive pseudoparabolic equations ⋮ Input-to-state stability for large-scale stochastic impulsive systems with state delay

Cites Work

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• Pulse coupled oscillators and the phase resetting curve
• Isochrons and phaseless sets
• Patterns of phase compromise in biological cycles
• Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons.
• The map with no predetermined firing order for the network of oscillators with time-delayed pulsatile coupling
• Dirac deltas and discontinuous functions
• A Computational and Geometric Approach to Phase Resetting Curves and Surfaces
• On Spiking Models for Synaptic Activity and Impulsive Differential Equations
• Parabolic Bursting in an Excitable System Coupled with a Slow Oscillation
• Event-based simulation of networks with pulse delayed coupling
• Global computation of phase-amplitude reduction for limit-cycle dynamics
• On the Phase Reduction and Response Dynamics of Neural Oscillator Populations
• Ordinary differential equations with delta function terms
• Complete Classification of the Macroscopic Behavior of a Heterogeneous Network of Theta Neurons
• Synchrony, stability, and firing patterns in pulse-coupled oscillators

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