Hopf bifurcation of the fractional-order Hindmarsh-Rose neuron model with time-delay

DOI10.1216/RMJ.2020.50.2213zbMath1480.34111OpenAlexW3120165686MaRDI QIDQ2219131

Yajuan Yu, Min Shi, Qi Xu

Publication date: 19 January 2021

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1609815819

zbMATH Keywords

stabilitytime-delayHopf bifurcationfractional calculusHindmarsh-Rose neuron model

Mathematics Subject Classification ID

Neural biology (92C20) Stability theory of functional-differential equations (34K20) Periodic solutions to functional-differential equations (34K13) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Bifurcation theory of functional-differential equations (34K18) Functional-differential equations with fractional derivatives (34K37)

Cites Work

• Lag synchronization of multiple identical Hindmarsh-Rose neuron models coupled in a ring structure
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative
• Effects of time delays on stability and Hopf bifurcation in a fractional ring-structured network with arbitrary neurons
• Abundant bursting patterns of a fractional-order Morris-Lecar neuron model
• Analysis of two- and three-dimensional fractional-order Hindmarsh-Rose type neuronal models
• Stability and Hopf Bifurcation Analysis in Hindmarsh–Rose Neuron Model with Multiple Time Delays
• Dynamical phases of the Hindmarsh-Rose neuronal model: Studies of the transition from bursting to spiking chaos
• METHODS OF THE QUALITATIVE THEORY FOR THE HINDMARSH–ROSE MODEL: A CASE STUDY – A TUTORIAL

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