FOLD–HOPF BIFURCATIONS OF THE ROSE–HINDMARSH MODEL WITH TIME DELAY
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Publication:2994869
DOI10.1142/S0218127411028490zbMath1210.34115MaRDI QIDQ2994869
Publication date: 29 April 2011
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
Neural biology (92C20) Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Bifurcation theory of functional-differential equations (34K18) Invariant manifolds of functional-differential equations (34K19)
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Bifurcation and Spike Adding Transition in Chay–Keizer 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 ⋮ Hopf Bifurcation Analysis of KdV–Burgers–Kuramoto Chaotic System with Distributed Delay Feedback ⋮ DYNAMICS OF A PREY-DEPENDENT DIGESTIVE MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL ⋮ Bogdanov-Takens singularity in the Hindmarsh-rose neuron with time delay ⋮ Traveling Waves Connecting Equilibrium and Periodic Orbit for a Delayed Population Model on a Two-Dimensional Spatial Lattice ⋮ Switching to Nonhyperbolic Cycles from Codimension Two Bifurcations of Equilibria of Delay Differential Equations ⋮ Stability and Hopf Bifurcation Analysis in Hindmarsh–Rose Neuron Model with Multiple Time Delays ⋮ APPLICATION OF A TWO-DIMENSIONAL HINDMARSH–ROSE TYPE MODEL FOR BIFURCATION ANALYSIS ⋮ \(1:3\) resonance and chaos in a discrete Hindmarsh-Rose model ⋮ INTERACTIONS OF TURING AND HOPF BIFURCATIONS IN AN ADDITIONAL FOOD PROVIDED DIFFUSIVE PREDATOR-PREY MODEL ⋮ DELAY-INDUCED DYNAMICAL TRANSITIONS IN SINGLE HINDMARSH–ROSE SYSTEM
Cites Work
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- From simple to simple bursting oscillatory behaviour via chaos in the Rose- Hindmarsh model for neuronal activity
- Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle
- Hopf bifurcation calculations in delayed systems with translational symmetry
- Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in \(\mathbb R^3\)
- Zero singularities of codimension two and three in delay differential equations
- LINEAR STABILITY AND HOPF BIFURCATION IN A TWO-NEURON NETWORK WITH THREE DELAYS
- Frustration, Stability, and Delay-Induced Oscillations in a Neural Network Model
- Dynamics of Small Neural Populations
- DYNAMICS AND DOUBLE HOPF BIFURCATIONS OF THE ROSE–HINDMARSH MODEL WITH TIME DELAY
- NEURAL EXCITABILITY, SPIKING AND BURSTING
- CLASSIFICATION OF BURSTING MAPPINGS
- HOPF BIFURCATION OF A TWO-NEURON NETWORK WITH DIFFERENT DISCRETE TIME DELAYS
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