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On bursting solutions near chaotic regimes in a neuron model

https://doi.org/10.3934/dcdss.2014.7.1363
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23/23 checkable references clean · checked 2026-07-22

Every reference with a DOI in the deposited reference list resolved to a known work in Crossref or DataCite at the dated check, and none carried a retraction, withdrawal, or removal notice.

2 without a DOI — not checked. A reference deposited without a DOI is never matched by title or guessed at; it stays outside the checked set, and this line discloses that.

The 23 checked references that resolve
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Synchronized Action of Synaptically Coupled Chaotic Model Neurons
resolves10.1007/s101890070012
Homoclinic bifurcations leading to the emergence of bursting oscillations in cell models
resolves10.1016/S0092-8240(05)81776-8
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resolves10.1152/jn.1999.82.1.382
Models of Respiratory Rhythm Generation in the Pre-Bötzinger Complex. I. Bursting Pacemaker Neurons
resolves10.1016/S0006-3495(83)84384-7
Minimal model for membrane oscillations in the pancreatic beta-cell
resolves10.1162/089976601300014655
Minimal Model for Intracellular Calcium Oscillations and Electrical Bursting in Melanotrope Cells of <i>Xenopus Laevis</i>
resolves10.1103/PhysRevLett.92.028101
Transitions to Synchrony in Coupled Bursting Neurons
resolves10.1137/1.9780898718195
Simulating, Analyzing, and Animating Dynamical Systems
resolves10.1016/0022-0396(79)90152-9
Geometric singular perturbation theory for ordinary differential equations
resolves10.1098/rspb.1984.0024
A model of neuronal bursting using three coupled first order differential equations
resolves10.1142/S0218127400000840
NEURAL EXCITABILITY, SPIKING AND BURSTING
resolves10.1016/S0022-0396(99)80018-7
Uniqueness and stability of periodic bursting solutions
resolves10.1142/S0218127409025080
DYNAMICS AND DOUBLE HOPF BIFURCATIONS OF THE ROSE–HINDMARSH MODEL WITH TIME DELAY
resolves10.1016/j.physd.2005.01.021
Reduction of a model of an excitable cell to a one-dimensional map
resolves10.1137/060655663
The Effect of Noise on β‐Cell Burst Period
resolves10.1103/PhysRevE.74.021917
Bursting induced by excitatory synaptic coupling in nonidentical conditional relaxation oscillators or square-wave bursters
resolves10.1016/S1874-575X(02)80024-8
Geometric Singular Perturbation Analysis of Neuronal Dynamics
resolves10.1103/PhysRevLett.86.183
Regularization of Synchronized Chaotic Bursts
resolves10.1152/ajpendo.1996.271.2.E362
Contributions of modeling to understanding stimulus-secretion coupling in pancreatic beta-cells
resolves10.1073/pnas.89.6.2471
Rhythmogenic effects of weak electrotonic coupling in neuronal models.
resolves10.1007/BF00198772
Rapid synchronization through fast threshold modulation
resolves10.1137/0151071
Chaotic Spikes Arising from a Model of Bursting in Excitable Membranes
resolves10.1007/978-90-481-9695-1_38
Transition Mechanisms Between Periodic and Chaotic Bursting Neurons
The 2 references without a DOI — listed, not checked
no DOI — not checkedJ. Rinzel, A formal classification of bursting mechanisms in excitable systems, <em>Proceedings of International Congress of Mathematics</em>, <strong>1</strong> (1987), 1578-1593.
no DOI — not checkedJ. Su, H. Perez and M. He, Regular bursting emerging from coupled chaotic neurons, <em>Discrete and Continuous Dynamical Systems</em>, supplemental issue, (2007), 946-955.
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