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Kazantsev V. B. Dynamic transformation of pulse signals in neuronal systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2004, vol. 12, iss. 6, pp. 118-128. DOI: 10.18500/0869-6632-2004-12-6-118-128
Dynamic transformation of pulse signals in neuronal systems
The dynamics of a neuron model with external pulse forcing in the form of bounded bursts is investigated. The processes of transformation of input pulse signal depending on the stimulus characteristics and neuron internal state are studied. A modified FitzHughNagumo system with a threshold manifold is used as the neuron model. It is found the neuron response provides selectivity on the number of acquired pulses (integrate-and-fire response) and on the inter-spike interval value (resonant response). The response signals are formed depending on the model parameters and represent either single pulses or pulse bursts with controllable number of constituent pulses.
- Nicolle J, Martin P, Vallas B, Fuchs P. From Neuron to Brain. Moskow: URSS; 2003. 672 p.
- Rubin AB. Biophysics: in 2 v. Moscow: Book House "University"; 2000. 486 p.
- Kandel ER, Schwartz JH, Jessell TM, editors. Principles of Neural Science. Third Edition. London: Prentice-Hall Intern. Inc; 1991. 1135 p.
- Scort А. Neuroscience: а mathematical premier. Berlin: Springer-Verlag; 2002. 576 p.
- Llinas R. I of the Vortex. From Neurons to Self. Cambridge, Massachusetts: MIT Press; 2002. 302 р.
- Brenner N, Strong SP, Koberle R, Bialek W, Steveninck RR. Synergy in a neural code. USA: Neural Computation. 2000;12(7):1531–1552. DOI: 10.1162/089976600300015259.
- Izhikevich EM. Neural excitability, spiking and bursting. Int. J. Bifurc. Chaos. 2000:10(6):1171–1266.
- Kazantsev VB, Nekorkin VI. Dynamics of oscillatory neurons. Informational aspects. In: Nonlinear Waves 2002. Nizhny Novgorod: IPF RAS, 2003. 29 р.
- Andronov AA, Witt, AA, Haykin, SE. Theory of vibrations. Moscow: Fizmatgiz; 1959. 916 р.
- Kuznetsov S.P. Dynamic Chaos (Lecture Course). Moscow: FML; 2001. 296 р.
- Pikovsky А, Rosenblum M, Kurths J. Synchronization. A Universal Concept in Nonlinear Sciences. Cambridge University Press. 2001. 433 p. DOI: 10.1017/CBO9780511755743.
- Glass L, Macky M. From Clock to Chaos. Rhythms of Life. Moscow: Mir; 1991. 248 p.
- FitzHugh В. Mathematical models оf excitation and propagation in nerve. In Biological Engineering. Schwan HP, editor. Introduction to Computational Cardiology, 1969. P. 1–85.
- Kaplan DT, Clay JR, Manning T, Glass L, Guevara MT, Shrier А. Subthreshold dynamics in periodically stimulated squid giant axons. Phys. Rev. Lett. 1996;76:4074–4077. DOI: 10.1103/PhysRevLett.76.4074/.
- Yoshino K, Nomura T, Pakdaman K, Sato S. Synthetic analysis of periodically stimulated excitable and oscillatory membrane models. Phys. Rev. Е. 1999;59(1):956. DOI: 10.1103/PhysRevE.59.956.
- Pakdaman K. Periodically forced leaky integrate-and-fire model. Phys. Rev. Е. 2001;63(4):041907. DOI: 10.1103/PhysRevE.63.041907.
- Eguia MC, Rabinovich МI, Abarbanel HDI. Information transmission and recovery in neuron communication channels. Phys. Rev. E. 2000:62(5):7111–7122. DOI: 10.1103/PhysRevE.62.7111.
- Nowotny Т, Zhigulin КР, Selverston А.Г, Abarbanel HDI, Rabinovich МI. Enhancement of synchronization in a hybrid neural circuit by spike-timing dependent plasticity. Journal Neuroscience. 2003;23(30):9776–9785. DOI: 10.1523/JNEUROSCI.23-30-09776.2003.
- Kazantsev VB. Selective communication and information processing by excitable systems. Phys. Rev. E. 2001;64(5):056210. DOI: 10.1103/PhysRevE.64.056210.
- Rinzel J, Ermentrout BB. in Methods in Neuronal Modeling. С. Koch C, Segev I, editors. Cambridge Massachussetts: MIT press, 1998. 251 p.
- Dmitrichev AS, Shapin DS, Kazantsev VB, Nekorkin VI. Dynamics of a neuron model with complex-threshold excitation. Mathematical Modeling. 2005;17(6):75–91.
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