Generation of periodic and chaotic bursting in an excitable cell model

DOI10.1007/BF00198918zbMath0805.92005MaRDI QIDQ1337287

Teresa Ree Chay, Yin Shui Fan

Publication date: 2 February 1995

Published in: Biological Cybernetics (Search for Journal in Brave)

zbMATH Keywords

burstingbifurcation diagramsmembrane potentialchaotic burstingaction potentialsexcitable cellslow-amplitude oscillationsneuronal cellsperiodic burstingPoincaré return map approach

Mathematics Subject Classification ID

Neural biology (92C20) Physiology (general) (92C30) Applications of dynamical systems (37N99)

Related Items (14)

Effects of quasi-steady-state reduction on biophysical models with oscillations ⋮ Propagation of periodic and chaotic action potential trains along nerve fibers ⋮ Chaotic electrical activity of living \(\beta\)-cells in the mouse pancreatic islet ⋮ Ion channels and the diversity of spontaneous firing in anterior pituitary corticotrophs: a dynamical analysis ⋮ Synchronization of coupled chaotic FitzHugh-Nagumo neurons via Lyapunov functions ⋮ Dynamics of autonomous stochastic resonance in neural period adding bifurcation scenarios ⋮ EFFECTS OF A PARAMETER MISMATCH ON THE SYNCHRONIZATION OF TWO COUPLED CHAOTIC OSCILLATORS ⋮ Qualitatively different bifurcation scenarios observed in the firing of identical nerve fibers ⋮ Recovering strange attractors from noisy interspike intervals of neuronal firings ⋮ Mathematical perspective of Hodgkin-Huxley model and bifurcation analysis ⋮ A SERIES OF BIFURCATION SCENARIOS IN THE FIRING PATTERN TRANSITIONS IN AN EXPERIMENTAL NEURAL PACEMAKER ⋮ Bifurcation scenarios of neural firing patterns across two separated chaotic regions as indicated by theoretical and biological experimental models ⋮ Nonlinear dynamics of the membrane potential of a bursting pacemaker cell ⋮ IDENTIFYING DISTINCT STOCHASTIC DYNAMICS FROM CHAOS: A STUDY ON MULTIMODAL NEURAL FIRING PATTERNS

Cites Work

• Bifurcations, burstings, chaos and crises in the Rose-Hindmarsh model for neuronal activity
• Abnormal discharges and chaos in a neuronal model system
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Chaos in a three-variable model of an excitable cell
• Dissection of a model for neuronal parabolic bursting
• Bifurcation and resonance in a model for bursting nerve cells
• From simple to complex oscillatory behaviour via intermittent chaos in the Rose-Hindmarsh model for neuronal activity
• From simple to simple bursting oscillatory behaviour via chaos in the Rose- Hindmarsh model for neuronal activity
• Crisis-induced chaos in the Rose-Hindmarsh model for neuronal activity
• Snap-back repellers imply chaos in \(\mathbb{R}^n\)
• Crisis transitions in excitable cell models
• Simple mathematical models with very complicated dynamics

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