Bifurcations, burstings, chaos and crises in the Rose-Hindmarsh model for neuronal activity

DOI10.1016/0960-0779(93)90029-ZzbMath0777.92003OpenAlexW1995472213MaRDI QIDQ686084

Arun V. Holden, Yin Shui Fan

Publication date: 12 December 1993

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

Full work available at URL: https://doi.org/10.1016/0960-0779(93)90029-z

zbMATH Keywords

action potentialexcitable membrane modelsbifurcation portraitburst generationchaos mechanismPoincare return mapsRose-Hindmarsh model

Mathematics Subject Classification ID

Neural biology (92C20) Bifurcation theory for ordinary differential equations (34C23) Applications of dynamical systems (37N99) Computational methods for problems pertaining to biology (92-08)

Related Items (21)

Generation of periodic and chaotic bursting in an excitable cell model ⋮ Effects of Time Delay on Burst Synchronization Transition of Neuronal Networks ⋮ Impulsive control and synchronization of chaotic Hhindmarsh-Rose models for neuronal activity ⋮ Chaotic behaviour of an acetylcholinesterase enzyme system ⋮ Impulsive pinning complex dynamical networks and applications to firing neuronal synchronization ⋮ Dynamics of autonomous stochastic resonance in neural period adding bifurcation scenarios ⋮ Qualitatively different bifurcation scenarios observed in the firing of identical nerve fibers ⋮ Complex bifurcation/chaotic behavior of acetylcholinesterase and cholineacetyltransferase enzymes system ⋮ Qualitative feature extractions of chaotic systems ⋮ QUALITATIVE RESONANCE OF SHIL'NIKOV-LIKE STRANGE ATTRACTORS, PART II: MATHEMATICAL ANALYSIS ⋮ A SERIES OF BIFURCATION SCENARIOS IN THE FIRING PATTERN TRANSITIONS IN AN EXPERIMENTAL NEURAL PACEMAKER ⋮ Dynamical mechanisms for sensitive response of aperiodic firing cells to external stimulation ⋮ An alternative bifurcation analysis of the Rose--Hindmarsh model ⋮ Bifurcation scenarios of neural firing patterns across two separated chaotic regions as indicated by theoretical and biological experimental models ⋮ On the Structure of the Bursting Region for a Neuronal Model ⋮ Homoclinical chaos and the period-adding route to complex non-chaotic attractors in fluidized bed catalytic reactors. ⋮ ChaosNet: A chaos based artificial neural network architecture for classification ⋮ Chaos synchronization of coupled neurons with gap junctions ⋮ IDENTIFYING DISTINCT STOCHASTIC DYNAMICS FROM CHAOS: A STUDY ON MULTIMODAL NEURAL FIRING PATTERNS ⋮ Burst and coherence resonance in Rose-Hindmarsh model induced by additive noise ⋮ Crisis transitions in excitable cell models

Cites Work

• 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
• Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle
• The transition from bursting to continuous spiking in excitable membrane models
• Chaotic Spikes Arising from a Model of Bursting in Excitable Membranes
• Unnamed Item

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