A Multiple Time Scale Coupling of Piecewise Linear Oscillators. Application to a Neuroendocrine System

DOI10.1137/140984464zbMath1329.34090OpenAlexW1988903077MaRDI QIDQ5249802

No author found.

Publication date: 12 May 2015

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/140984464

zbMATH Keywords

coupled oscillatorspiecewise linear systemsrelaxation oscillationsslow-fast dynamicsGnRH secretion

Mathematics Subject Classification ID

Neural biology (92C20) Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Discontinuous ordinary differential equations (34A36) Qualitative investigation and simulation of ordinary differential equation models (34C60) General biology and biomathematics (92B05) Systems with slow and fast motions for nonlinear problems in mechanics (70K70) Relaxation oscillations for ordinary differential equations (34C26)

Related Items (7)

Estimation of Synaptic Conductance in the Spiking Regime for the McKean Neuron Model ⋮ Canards in a minimal piecewise-linear square-wave burster ⋮ Symmetric coupling of multiple timescale systems with mixed-mode oscillations and synchronization ⋮ Canard Limit Cycles for Piecewise Linear Liénard Systems with Three Zones ⋮ Mixed-mode oscillations in a piecewise linear system with multiple time scale coupling ⋮ Canards, Folded Nodes, and Mixed-Mode Oscillations in Piecewise-Linear Slow-Fast Systems ⋮ Sequential Escapes and Synchrony Breaking for Networks of Bistable Oscillatory Nodes

Cites Work

• Unnamed Item
• Hopf-like bifurcations in planar piecewise linear systems
• Limit cycles for planar piecewise linear differential systems via first integrals.
• Geometric properties of a class of piecewise affine biological network models
• Piecewise-smooth dynamical systems. Theory and applications
• On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry
• Nagumo's equation
• Canards in piecewise-linear systems: explosions and super-explosions
• Pattern Formation in a Model of an Injured Nerve Fiber
• Existence of a Reversible T-Point Heteroclinic Cycle in a Piecewise Linear Version of the Michelson System
• Neuronal Networks with Gap Junctions: A Study of Piecewise Linear Planar Neuron Models
• Multiple impulse solutions to McKean's caricature of the nerve equation. II. Stability
• Reality of chaos in the double scroll circuit: A computer-assisted proof
• BIFURCATION SETS OF SYMMETRICAL CONTINUOUS PIECEWISE LINEAR SYSTEMS WITH THREE ZONES
• The McKean's Caricature of the Fitzhugh--Nagumo Model I. The Space-Clamped System
• Phase portraits of planar control systems
• Mixed-Mode Oscillations in a Multiple Time Scale Phantom Bursting System
• Bifurcation Sets of Continuous Piecewise Linear Systems with Two Zones
• Introduction to the Qualitative Theory of Differential Systems
• Mathematical Modeling of the GnRH Pulse and Surge Generator
• On simplifying and classifying piecewise-linear systems
• Foliation-Based Parameter Tuning in a Model of the GnRH Pulse and Surge Generator
• Multiple impulse solutions to McKean's caricature of the nerve equation. I—existence

This page was built for publication: A Multiple Time Scale Coupling of Piecewise Linear Oscillators. Application to a Neuroendocrine System