DYNAMICS AND DOUBLE HOPF BIFURCATIONS OF THE ROSE–HINDMARSH MODEL WITH TIME DELAY

DOI10.1142/S0218127409025080zbMath1182.34104MaRDI QIDQ5305154

Suqi Ma, Qishai Lu, Zhao-sheng Feng

Publication date: 19 March 2010

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

zbMATH Keywords

Hopf bifurcationnormal formelliptic functionautonomous systemRose-Hindmarsh modelcenter manifold method

Mathematics Subject Classification ID

Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Stability theory of functional-differential equations (34K20) 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)

Related Items (16)

Delay-induced Hopf bifurcation in a noise-driven excitable neuron model ⋮ Bifurcation and Spike Adding Transition in Chay–Keizer Model ⋮ Random attractor for stochastic Hindmarsh-Rose equations with multiplicative noise ⋮ Synthesizing attractors of Hindmarsh-Rose neuronal systems ⋮ Delay-induced mixed-mode oscillations in a 2D Hindmarsh-Rose-type model ⋮ Exponential synchronization of memristive Hindmarsh-Rose neural networks ⋮ Traveling wave solutions of diffusive Hindmarsh-Rose-type equations with recurrent neural feedback ⋮ Synchronization of boundary coupled Hindmarsh-rose neuron network ⋮ Random attractor for stochastic Hindmarsh-Rose equations with additive noise ⋮ FOLD–HOPF BIFURCATIONS OF THE ROSE–HINDMARSH MODEL WITH TIME DELAY ⋮ On bursting solutions near chaotic regimes in a neuron model ⋮ Desynchronization in synchronous multi-coupled chaotic neurons by mix-adaptive feedback control ⋮ DYNAMICS OF A PREY-DEPENDENT DIGESTIVE MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL ⋮ Global dynamics of nonautonomous Hindmarsh-Rose equations ⋮ EXPONENTIAL ATTRACTOR FOR HINDMARSH-ROSE EQUATIONS IN NEURODYNAMICS ⋮ DELAY-INDUCED DYNAMICAL TRANSITIONS IN SINGLE HINDMARSH–ROSE SYSTEM

Uses Software

• DDE-BIFTOOL

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• A simple global characterization for normal forms of singular vector fields
• From simple to simple bursting oscillatory behaviour via chaos in the Rose- Hindmarsh model for neuronal activity
• Limit cycles, tori, and complex dynamics in a second-order differential equation with delayed negative feedback
• Restrictions and unfolding of double Hopf bifurcation in functional differential equations
• Double Hopf bifurcation for van der Pol-Duffing oscillator with parametric delay feedback control
• STABILITY SWITCHES OF TIME-DELAYED DYNAMIC SYSTEMS WITH UNKNOWN PARAMETERS
• ANTI-PHASE SYNCHRONIZATION OF INHIBITORILY COUPLED NEURONS
• DELAY-INDEPENDENT STABILITY OF RETARDED DYNAMIC SYSTEMS OF MULTIPLE DEGREES OF FREEDOM
• HOPF BIFURCATION OF TIME-DELAY LIENARD EQUATIONS
• Threshold dynamics in a delayed SIS epidemic model

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