Crisis transitions in excitable cell models

DOI10.1016/0960-0779(93)90047-5zbMath0855.34051OpenAlexW2050177853MaRDI QIDQ1321705

Teresa Ree Chay, Yin Shui Fan

Publication date: 8 May 1994

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0960-0779(93)90047-5

zbMATH Keywords

dissipative dynamical systemsPoincaré mapschaotic attractorbifurcation diagramsexcitable cellsinterior crisis phenomenanumber of unstable periodic orbits on chaotic attractor

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Medical applications (general) (92C50) Complex behavior and chaotic systems of ordinary differential equations (34C28) Attractors of solutions to ordinary differential equations (34D45)

Related Items (5)

Generation of periodic and chaotic bursting in an excitable cell model ⋮ A chaotic bursting-spiking transition in a pancreatic beta-cells system: observation of an interior glucose-induced crisis ⋮ A SERIES OF BIFURCATION SCENARIOS IN THE FIRING PATTERN TRANSITIONS IN AN EXPERIMENTAL NEURAL PACEMAKER ⋮ An alternative bifurcation analysis of the Rose--Hindmarsh model ⋮ Nonlinear dynamics of the membrane potential of a bursting pacemaker cell

Cites Work

• Bifurcations, burstings, chaos and crises in the Rose-Hindmarsh model for neuronal activity
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Chaos in a three-variable model of an excitable cell
• 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 \(\mathbb{R}^n\)
• Simple mathematical models with very complicated dynamics

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