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Neural Computing and Applications

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01.04.2016 | Original Article

Bifurcation study of neuron firing activity of the modified Hindmarsh–Rose model

Erschienen in: Neural Computing and Applications | Ausgabe 3/2016

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Abstract

In this paper, the effects of different parameters on the dynamic behavior of the nonlinear dynamical system are investigated based on modified Hindmarsh–Rose neural nonlinear dynamical system model. We have calculated and analyzed dynamic characteristics of the model under different parameters by using single parameter bifurcation diagram, time response diagram and two parameter bifurcation diagram. The results show that the period-adding bifurcation (with or without chaos), period-doubling bifurcation and intermittent chaos phenomenon (periodic and intermittent chaotic) can be observed more clearly and directly from the two parameter bifurcation diagram, and the optimal parameters matching interval can also be found easily.

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Shou TD (2006) Neurobiology. Higher Education Press, Beijing

Hodgkin AL, Huxley AF (1952) The components of membrane conductance in the giant axon of Loligo. J Physiol 116:473–496CrossRef

Hodgkin AL, Huxley AF (1952) Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J Physiol 116:449–472CrossRef

Hodgkin AL, Huxley AF (1952) A quantitative description of membrane and its application to conduction and excitation in nerve. J Physiol 117:500–544CrossRef

Izhikevich EM (2007) Dynamical systems in neuroscience: the geometry of excitability and bursting. MIT Press, Cambridge

Morris C, Lecar H (1981) Voltage oscillations in the blamable giant muscle fiber. Biophys J 35:193–213CrossRef

Chay TR, Keizer J (1983) Minimal model for membrane oscillations in the pancreatic beta-cell. Biophys J 42:181–190CrossRef

Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond Ser B 221:87–102CrossRef

Rinzel J, Lee YS (1987) Dissection of a model for neuronal parabolic bursting. J Math Biol 25:653–675MathSciNetCrossRefMATH

10.

Grubelnk V, Larsen AZ, Kummer U et al (2001) Mitochondria regulates the amplitude of simple and complex calcium oscillations. Biophys Chem 94:59–74CrossRef

11.

Ge ML, Guo HY, Wang GJ, Yan WL (2003) Research for synchronous oscillation on electrically coupled Chay neurons. Acta Biophys Sin 19(2):135–140

12.

Perc M, Marhl M (2004) Synchronization of regular and chaotic oscillations: the role of local divergence and the slow passage effect—a case study on calcium oscillations. Int J Bifurc Chaos Appl Sci Eng 14(8):2735–2751MathSciNetCrossRefMATH

13.

Izhikevich EM, Desai NS, Walcott EC et al (2003) Bursts as a unit of neural information: selective communication via resonance. Trends Neurosci 26(3):161–167CrossRef

14.

Ricardo AL, Rafael MG, Héctor P et al (2010) High order sliding-mode dynamic control for chaotic intracellular calcium oscillations. Nonlinear Anal Real World Appl 11:217–231MathSciNetCrossRefMATH

15.

Liu XL, Liu SQ (2012) Codimension-two bifurcations analysis in two-dimensional Hindmarsh–Rose model. Nonlinear Dyn 67:847–857CrossRefMATH

16.

Zhou J, Wu QJ, Xiang L (2012) Impulsive pinning complex dynamical networks and applications to firing neuronal synchronization. Nonlinear Dyn 69:1393–1403MathSciNetCrossRefMATH

17.

Ji QB, Lu QS, Yang ZQ et al (2008) Bursting Ca²⁺ oscillations and synchronization in coupled cells. Chin Phys Lett 25:3879–3883CrossRef

18.

Nchange AK, Kepseu WD, Woafo P (2008) Noise induced intercellular propagation of calcium waves. Phys A 387:2519–2525CrossRef

19.

Zhang F, Lu QS, Su JZ (2009) Transition in complex calcium bursting induced by IP3 degradation. Chaos Solitons Fractals 5:2285–2290CrossRef

20.

Zheng YH, Lu QS (2008) Synchronization in ring coupled chaotic neurons with time delay. J Dyn Control 6(3):208–212MathSciNet

21.

Wang HX, Wang QY, Lu QS (2011) Bursting oscillations, bifurcation and synchronization in neuronal systems. Chaos Solitons Fractals 44(8):667–675CrossRefMATH

22.

Nimet D, Imail Ö, Recai K (2012) Experimental realizations of the HR neuron model with programmable hardware and synchronization applications. Nonlinear Dyn 70:2343–2358MathSciNetCrossRef

23.

Ma SQ, Lu QS, Feng ZS (2010) Synchrony and lag synchrony on a neuron model coupling with time delay. Int J Nonlinear Mech 45(6):659–665CrossRef

24.

Li B, He ZM (2014) Bifurcations and chaos in a two-dimensional discrete Hindmarsh–Rose model. Nonlinear Dyn 76:697–715MathSciNetCrossRefMATH

25.

Shilnikov A, Marina K (2008) Methods of the qualitative theory for the Hindmarsh–Rose model: a case study—a tutorial. Int J Bifurc Chaos 18(8):2141–2168MathSciNetCrossRefMATH

26.

Djeundam Dtchetgnia SR, Yamapi R, Filatrella G, Kofane TC (2015) Stability of the synchronized network of Hindmarsh–Rose neuronal models with nearest and global couplings. Commun Nonlinear Sci Numer Simul 22(1):545–563MathSciNetCrossRefMATH

27.

Zhang DG, Zhang Q, Zhu XY (2015) Exploring a type of central pattern generator based on Hindmarsh–Rose model: from theory to application. Int J Neural Syst 25(1):1450028 (15 pages)CrossRef

28.

Tsumoto K, Kitajima H, Yoshinaga T (2006) Bifurcations in Morris–Lecar neuron model. Neurocomputing 69:293–316CrossRef

29.

Keplinger K, Wackerbauer R (2014) Transient spatiotemporal chaos in the Morris–Lecar neuronal ring network. Chaos 24(1):385–397MathSciNetCrossRef

30.

Song SL (2010) The transition rules of injured nerve spontaneous discharge rhythm under the dual parameters. Shaanxi Normal University, Xi’an

31.

Krasimira TA, Hinke MO, Thorsten R et al (2010) Full system bifurcation analysis of endocrine bursting models. J Theor Biol 264(4):1133–1146MathSciNetCrossRef

Titel: Bifurcation study of neuron firing activity of the modified Hindmarsh–Rose model
Publikationsdatum: 01.04.2016
Erschienen in: Neural Computing and Applications / Ausgabe 3/2016
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-015-1892-1

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