Homoclinic organization in the Hindmarsh–Rose model: A three parameter study
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Publication:3303879
DOI10.1063/1.5138919zbMath1437.92021OpenAlexW3026479466WikidataQ96120026 ScholiaQ96120026MaRDI QIDQ3303879
Roberto Barrio, Lucía Pérez, Santiago Ibáñez
Publication date: 4 August 2020
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.5138919
Neural biology (92C20) Qualitative investigation and simulation of ordinary differential equation models (34C60)
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Cites Work
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- Mathematical foundations of neuroscience
- Homoclinic orbits of the FitzHugh-Nagumo equation: the singular-limit
- Bifurcation phenomena appearing in the Lotka-Volterra competition equations: A numerical study
- Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle
- Abundance of strange attractors
- Full system bifurcation analysis of endocrine bursting models
- Parameter-sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh-Rose model
- Nilpotent singularities and chaos: tritrophic food chains
- Spike-adding structure in fold/hom bursters
- Dynamical systems analysis of spike-adding mechanisms in transient bursts
- Coupling leads to chaos
- Belyakov Homoclinic Bifurcations in a Tritrophic Food Chain Model
- Mixed-mode bursting oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster
- Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons
- Mixed-Mode Oscillations with Multiple Time Scales
- Canards of Folded Saddle-Node Type I
- Bifurcations ofn-homoclinic orbits in optically injected lasers
- Brussellator Isolas
- Homoclinic Orbits of the FitzHugh–Nagumo Equation: Bifurcations in the Full System
- When Shil'nikov Meets Hopf in Excitable Systems
- Dynamical phases of the Hindmarsh-Rose neuronal model: Studies of the transition from bursting to spiking chaos
- Chaotic Spikes Arising from a Model of Bursting in Excitable Membranes
- Unpeeling a Homoclinic Banana in the FitzHugh--Nagumo System
- CLOSED CURVES OF GLOBAL BIFURCATIONS IN CHUA'S EQUATION: A MECHANISM FOR THEIR FORMATION
- BIFURCATION, BURSTING AND SPIKE GENERATION IN A NEURAL MODEL
- Codimension-Two Homoclinic Bifurcations Underlying Spike Adding in the Hindmarsh--Rose Burster
- ON THE NUMERICAL CONTINUATION OF ISOLAS OF EQUILIBRIA
- METHODS OF THE QUALITATIVE THEORY FOR THE HINDMARSH–ROSE MODEL: A CASE STUDY – A TUTORIAL
- The Period Adding and Incrementing Bifurcations: From Rotation Theory to Applications
- A Period-Adding Phenomenon
- Elements of applied bifurcation theory
- Resonant homoclinic flip bifurcations
- Death of period-doublings: Locating the homoclinic-doubling cascade
- Homoclinic-doubling cascades.
