Symmetric Fold/Super-Hopf Bursting, Chaos and Mixed-Mode Oscillations in Pernarowski Model of Pancreatic Beta-Cells

DOI10.1142/S0218127416300226zbMath1347.34076MaRDI QIDQ2827014

Haniyeh Fallah

Publication date: 12 October 2016

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

chaosmixed-mode oscillationscanardperiod doubling cascades of canardspolynomial Pernarowski modelsymmetric bursting

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Cell biology (92C37) Qualitative investigation and simulation of ordinary differential equation models (34C60) Complex behavior and chaotic systems of ordinary differential equations (34C28) Canard solutions to ordinary differential equations (34E17)

Related Items (12)

Mixed mode oscillations induced by bi-stability and fractal basins in the FGP plate under slow parametric and resonant external excitations ⋮ Complex periodic bursting structures in the Rayleigh-van der Pol-Duffing oscillator ⋮ Elimination of spiral waves in a one-layer and two-layer network of pancreatic beta cells using a periodic stimuli ⋮ The hidden, period-adding, mixed-mode oscillations and control in a HR neuron under electromagnetic induction ⋮ Complex bursting dynamics in the cubic-quintic Duffing-van der Pol system with two external periodic excitations ⋮ Bursting Oscillations and Mixed-Mode Oscillations in Driven Liénard System ⋮ A novel memristor-based dynamical system with multi-wing attractors and symmetric periodic bursting ⋮ Periodic bursting behaviors induced by pulse-shaped explosion or non-pulse-shaped explosion in a van der Pol-Mathieu oscillator with external excitation ⋮ A chaotic bursting-spiking transition in a pancreatic beta-cells system: observation of an interior glucose-induced crisis ⋮ Fractal structures in centrifugal flywheel governor system ⋮ A dual memristive Wien-bridge chaotic system with variable amplitude and frequency ⋮ Complex Bursting Patterns in a van der Pol–Mathieu–Duffing Oscillator

Uses Software

• XPPAUT

Cites Work

• Unnamed Item
• Unnamed Item
• Symmetric bursting behaviors in the generalized FitzHugh-Nagumo model
• Period-doubling cascades of canards from the extended Bonhoeffer-van der Pol oscillator
• 3-torus, quasi-periodic bursting, symmetric subhopf/fold-cycle bursting, subhopf/fold-cycle bursting and their relation
• Symmetric bursting of focus-focus type in the controlled Lorenz system with two time scales
• Analysis of bursting in a thalamic neuron model
• Topological and phenomenological classification of bursting oscillations
• Different types of bursting calcium oscillations in non-excitable cells
• Dynamical systems analysis of spike-adding mechanisms in transient bursts
• Bursting behavior in a non-smooth electric circuit
• Mixed-mode bursting oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster
• Mixed-Mode Oscillations with Multiple Time Scales
• Properties of a Bursting Model with Two Slow Inhibitory Variables
• Slow Passage Through a Hopf Bifurcation: From Oscillatory to Steady State Solutions
• Simulating, Analyzing, and Animating Dynamical Systems
• Canard Induced Mixed-Mode Oscillations in a Medial Entorhinal Cortex Layer II Stellate Cell Model
• SYNCHRONIZATION OF REGULAR AND CHAOTIC OSCILLATIONS: THE ROLE OF LOCAL DIVERGENCE AND THE SLOW PASSAGE EFFECT — A Case Study on Calcium Oscillations
• BIFURCATION, BURSTING AND SPIKE GENERATION IN A NEURAL MODEL
• Codimension-Two Homoclinic Bifurcations Underlying Spike Adding in the Hindmarsh--Rose Burster
• Mixed-Mode Oscillations in a Multiple Time Scale Phantom Bursting System
• Computing Slow Manifolds of Saddle Type
• NEURAL EXCITABILITY, SPIKING AND BURSTING
• Canards in \(\mathbb{R}^3\)

This page was built for publication: Symmetric Fold/Super-Hopf Bursting, Chaos and Mixed-Mode Oscillations in Pernarowski Model of Pancreatic Beta-Cells