The Solution of the Second Peskin Conjecture and Developments

DOI10.1007/978-3-319-26630-5_1zbMath1416.37072OpenAlexW2465475690MaRDI QIDQ5223302

Marat U. Akhmet

Publication date: 17 July 2019

Published in: Mathematical Modeling and Applications in Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-26630-5_1

zbMATH Keywords

bifurcationsynchronizationcardiac pacemaker model

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Medical applications (general) (92C50) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Physiological flow (92C35) Synchronization of solutions to ordinary differential equations (34D06)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Self-synchronization of the integrate-and-fire pacemaker model with continuous couplings
• Perturbations and Hopf bifurcation of the planar discontinuous dynamical system
• Nonlinear hybrid continuous/discrete-time models
• Chemical oscillations, waves, and turbulence
• The behavior of rings of coupled oscillators
• Collective synchronization of pulse-coupled oscillators and excitable units
• A simple model for phase locking of biological oscillators
• Weakly connected neural networks
• Bifurctions, patterns and symmetry. Selected papers dedicated to the memory of John David Crawford
• Mathematical biology. Vol. 1: An introduction.
• Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities
• Similar NonLeaky Integrate-and-Fire Neurons with Instantaneous Couplings Always Synchronize
• Synchronization of the Cardiac Pacemaker Model with Delayed Pulse-coupling
• Analysis of biological integrate-and-fire oscillators
• Synchronization of Pulse-Coupled Biological Oscillators
• The simplest problem in the collective dynamics of neural networks: is synchrony stable?
• Principles of Discontinuous Dynamical Systems
• Parabolic Bursting in an Excitable System Coupled with a Slow Oscillation
• Collective synchronisation in lattices of nonlinear oscillators with randomness
• Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere
• Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets
• On Chains of Oscillators Forced at One End
• Oscillator Death in Systems of Coupled Neural Oscillators
• On quasi stability for impulsive differential systems
• Comparison principle for impulsive differential equations with variable times and stability theory
• Global stability results for impulsive differential equations
• Spiking Neuron Models
• Impulsive differential equations with variable times
• Pulse-Coupled Decentral Synchronization
• A new model for simple neural nets and its application in the design of a neural oscillator
• Exploring complex networks
• Synchrony, stability, and firing patterns in pulse-coupled oscillators

This page was built for publication: The Solution of the Second Peskin Conjecture and Developments