BIFURCATIONS IN TWO-DIMENSIONAL HINDMARSH–ROSE TYPE MODEL

DOI10.1142/S0218127407017707zbMath1142.37380OpenAlexW1987869613MaRDI QIDQ3499171

Hiroshi Kawakami, Hiroshi Fujii, Kazuyuki Aihara, Shigeki Tsuji, Tetsushi Ueta

Publication date: 28 May 2008

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

Full work available at URL: https://doi.org/10.1142/s0218127407017707

zbMATH Keywords

bifurcation theoryHindmarsh-Rose modelFitzHugh-Nagumo modelClass I and Class 2 neuronsneuronal excitability and spiking

Mathematics Subject Classification ID

Neural biology (92C20) Dynamical systems in biology (37N25) Bifurcation theory for ordinary differential equations (34C23) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (17)

Analysis of two- and three-dimensional fractional-order Hindmarsh-Rose type neuronal models ⋮ Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model ⋮ Unnamed Item ⋮ Effects of self-coupling and asymmetric output on metastable dynamical transient firing patterns in arrays of neurons with bidirectional inhibitory coupling ⋮ Idealized multiple-timescale model of cortical spreading depolarization initiation and pre-epileptic hyperexcitability caused by \(\mathrm{Na_V}1.1/ SCN1A\) mutations ⋮ Delay-induced mixed-mode oscillations in a 2D Hindmarsh-Rose-type model ⋮ Codimension-two bifurcation analysis in two-dimensional Hindmarsh-Rose model ⋮ Traveling wave solutions of diffusive Hindmarsh-Rose-type equations with recurrent neural feedback ⋮ Explicit transversality conditions and local bifurcation diagrams for bogdanov-Takens bifurcation on center manifolds ⋮ Changes of Firing Rate Induced by Changes of Phase Response Curve in Bifurcation Transitions ⋮ 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 ⋮ Bifurcations and chaos in a two-dimensional discrete Hindmarsh-Rose model ⋮ A Novel Threshold Across which the Negative Stimulation Evokes Action Potential Near a Saddle-Node Bifurcation in a Neuronal Model with Ih Current ⋮ APPLICATION OF A TWO-DIMENSIONAL HINDMARSH–ROSE TYPE MODEL FOR BIFURCATION ANALYSIS ⋮ \(1:3\) resonance and chaos in a discrete Hindmarsh-Rose model ⋮ Emergence of Turing patterns and dynamic visualization in excitable neuron model

Cites Work

• On the concept of attractor
• Relaxation oscillations including a standard chase on French ducks
• NEURAL EXCITABILITY, SPIKING AND BURSTING

This page was built for publication: BIFURCATIONS IN TWO-DIMENSIONAL HINDMARSH–ROSE TYPE MODEL