APPLICATION OF A TWO-DIMENSIONAL HINDMARSH–ROSE TYPE MODEL FOR BIFURCATION ANALYSIS

DOI10.1142/S0218127413500557zbMath1270.34121OpenAlexW2162745417MaRDI QIDQ2845180

Yi-Ru Lin, Chang-Yuan Cheng, Shyan-Shiou Chen

Publication date: 22 August 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127413500557

zbMATH Keywords

bifurcation analysisneuro-computational featuresspike-and-reset conditions

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Neural biology (92C20) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (10)

Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model ⋮ Delay-induced mixed-mode oscillations in a 2D Hindmarsh-Rose-type model ⋮ Traveling wave solutions of diffusive Hindmarsh-Rose-type equations with recurrent neural feedback ⋮ 1:2 and 1:4 resonances in a two-dimensional discrete Hindmarsh-Rose model ⋮ Bifurcation analysis of a two-dimensional discrete Hindmarsh-Rose type model ⋮ Delay-induced spiking dynamics in integrate-and-fire neurons ⋮ A Novel Threshold Across which the Negative Stimulation Evokes Action Potential Near a Saddle-Node Bifurcation in a Neuronal Model with Ih Current ⋮ Coexistence of firing patterns and its control in two neurons coupled through an asymmetric electrical synapse ⋮ \(1:3\) resonance and chaos in a discrete Hindmarsh-Rose model ⋮ Emergence of Turing patterns and dynamic visualization in excitable neuron model

Cites Work

• Chaos in a three-variable model of an excitable cell
• The transition from bursting to continuous spiking in excitable membrane models
• FOLD–HOPF BIFURCATIONS OF THE ROSE–HINDMARSH MODEL WITH TIME DELAY
• COMPLEX BIFURCATION STRUCTURES IN THE HINDMARSH–ROSE NEURON MODEL
• BIFURCATIONS IN TWO-DIMENSIONAL HINDMARSH–ROSE TYPE MODEL
• Bifurcation Analysis of a General Class of Nonlinear Integrate-and-Fire Neurons
• ANALYSIS OF THE TAKENS–BOGDANOV BIFURCATION ON m-PARAMETERIZED VECTOR FIELDS
• 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
• Observation of a continuous interior crisis in the Hindmarsh–Rose neuron model

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