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Dynamics in the Parameter Space of a Neuron Model |
| Paulo C. Rech** |
| Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil |
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Paulo C. Rech 2012 Chin. Phys. Lett. 29 060506 |
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Abstract Some two-dimensional parameter-space diagrams are numerically obtained by considering the largest Lyapunov exponent for a four-dimensional thirteen-parameter Hindmarsh–Rose neuron model. Several different parameter planes are considered, and it is shown that depending on the combination of parameters, a typical scenario can be preserved: for some choice of two parameters, the parameter plane presents a comb-shaped chaotic region embedded in a large periodic region. It is also shown that there exist regions close to these comb-shaped chaotic regions, separated by the comb teeth, organizing themselves in period-adding bifurcation cascades.
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| Keywords:
05.45.-a
05.45.Pq
05.45.Ac
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Received: 03 February 2012
Published: 31 May 2012
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| PACS: |
05.45.-a
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(Nonlinear dynamics and chaos)
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05.45.Pq
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(Numerical simulations of chaotic systems)
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05.45.Ac
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(Low-dimensional chaos)
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| [1] Hindmarsh J and Rose R 1984 Proc. R. Soc. London B 221 87[2] Hodgkin A L and Huxley A F 1952 J. Physiol. Lond. 117 500[3] Herz A V M, Gollisch T, Machens C K and Jaeger D 2006 Science 314 80[4] Pinto R D, Varona P, Volkovskii A R, Szücs A, Abarbanel H D I and Rabinovich M I 2000 Phys. Rev. E 62 2644[5] Yu H and Peng J 2006 Chaos Solitons Fractals 29 342[6] González-Miranda J M 2007 Int. J. Bifur. Chaos 17 3071[7] Storace M, Linaro D and de Lange E 2008 Chaos 18 033128[8] Innocenti G and Genesio R 2009 Chaos 19 023124[9] Moujahid A, d'Anjou A, Torrealdea F J and Torrealdea F 2011 Chaos Solitons Fractals 44 929[10] Barrio R and Shilnikov A 2011 J. Math. Neurosci. 1 6[11] Linaro D, Poggi T and Storace M 2010 Phys. Lett. A 374 4589[12] Rech P C 2011 Phys. Lett. A 375 1461[13] Wolf A, Swift J B, Swinney H L and Vastano J A 1985 Physica D 16 285 |
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