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Alidousti J, Ghaziani RK (2017) Spiking and bursting of a fractional order of the modified FitzHugh-Nagumo neuron model Mathematical Models and Computer Simulations 9:390-403

References and models cited by this paper

References and models that cite this paper

Diethelm K (2010) The Analysis of Fractional Differential Equations

Ehibilik AI, Borisyuk RM, Roose D (1992) Numerical Bifurcation Analysis of a Model of Coupled Neural Oscillators International Series Of Numerical Mathematics 104:215-228

Ermentrout B (1996) Type I membranes, phase resetting curves, and synchrony. Neural Comput 8:979-1001 [PubMed]

Ermentrout GB, Kopell N (1986) Parabolic bursting in an excitable system coupled with a slow oscillation. Siam J Appl Math 46:233-253

Fitzhugh R (1961) Impulses and Physiological States in Theoretical Models of Nerve Membrane. Biophys J 1:445-66 [PubMed]

Hifer R (2000) Application of Fractional Calculus in Physics

Hodgkin AL (1948) The local electric changes associated with repetitive action in a non-medullated axon. J Physiol 107:165-81 [PubMed]

HODGKIN AL, HUXLEY AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500-44 [Journal] [PubMed]

   Squid axon (Hodgkin, Huxley 1952) (LabAXON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (NEURON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SNNAP) [Model]
   Squid axon (Hodgkin, Huxley 1952) used in (Chen et al 2010) (R language) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SBML, XPP, other) [Model]

Hoppensteadt FC, Izhikevich EM (1997) Weakly Connected Neural Networks :90

Izhikevich E (2000) Subcritical elliptic bursting of Bautin type SIAM J Appl Math 60:503-535

Izhikevich EM (1999) Class 1 neural excitability, conventional synapses, weakly connected networks, and mathematical foundations of pulse-coupled models. IEEE Trans Neural Netw 10:499-507 [Journal] [PubMed]

Izhikevich EM (2000) Neural excitability, spiking and bursting Int J Bifurcat Chaos Appl Sci Eng 10:1171-1266

Kilbas S (2006) Lamotrigine-induced leucopenia. Epileptic Disord 8:317 [PubMed]

Kumar P,Agrawal OP (2006) An approximate method for numerical solution of fractional differential equations Signal Proccess 6:2602-2610

Li CP,Wang YH (2009) Numerical algorithm based on Adomian decomposition for fractional differential equations Comput. Math. Appl. 57:1627-1681

Magin RL (2004) Fractional calculus in bioengineering. Crit Rev Biomed Eng 32:1-104 [PubMed]

Mishra D, Yadav A, Kalra PK (2004) Chaotic Behavior in Neural Network and FitzHugh-Nagumo Neuronal Model LNCS 3316 ICONIP-2004 :868-887

Monje CA,Chen YQ,Vinagre BM,Xue DY,Feliu V (2010) Fractional Order Systems and Controls: Fundamentals and Applications

Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35:193-213 [Journal] [PubMed]

   Morris-Lecar model of the barnacle giant muscle fiber (Morris, Lecar 1981) [Model]

Petras I () Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation

Rinzel J (1980) Models in neurobiology. Nonlinear Phenomena in Physics and Biology., Enns RH:Jones BL:Miura RM:Rangnekar SS, ed. pp.347

Rinzel J (1987) A formal classification of bursting mechanisms in excitable systems. Mathematical Topics in Population Biology, Morphogenesis, and Neurosciences., Teramoto E:Yamaguti M, ed. pp.267

Rinzel J, Ermentrout GB (1989) Analysis of neuronal excitability and oscillations Methods In Neuronal Modeling: From Synapses To Networks, Koch C:Segev I, ed. pp.135

Shi M,Wang Z (2014) Abundant bursting patterns of a fractional-order Morris-Lecar neuron model Commun Nonlinear Sci Numer Simul 19:1956-1969

Wang H,Wang Q (2011) Bursting oscillations, bifurcation and synchronization in neuronal systems Chaos, Solitons, Fractals 44:667-675

Westerlund S,Ekstam L (1994) Capacitor theory IEEE Trans Dielectr Electr Insul 1(8):26-39

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