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Section DYNAMICS IN LIFE SCIENCES, NEUROSCIENCE APPLICATIONS WORKSHOP
Extreme Events in Bursting Neurons
Arindam Mishra1,2, Suman Saha1, Hilda Cerdeira3, Syamal K. Dana1*
1 CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032, India;
2 Department of Physics, Jadavpur University, Kolkata 700032, India;
3 Instituto de Física Teórica, UNESP, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, 01140-070 Sao Paulo, Brazil.
* Presenting e-mail: syamaldana@gmail.com
Coexisting coherent and noncoherent subpopulations in networks of identical oscillators hitherto called as chimera states [1-3] is intriguing, however, existence of such pattern is observed in many systems under both nonlocal coupling and global coupling. We reported [4] such chimera-like states in globally coupled oscillators under the influence of both attractive and repulsive coupling, which is a common type of coupling in biological networks, in other words, there they are called as excitatory and inhibitory coupling. We further extended this work to an ensemble of bursting neurons taking the Hindamarsh-model as the dynamical units, however, using purely repulsive global coupling. We find clear evidence of chimera-like states in a parameter space. Surprisingly, in the noncoherent subgroup of oscillators, we observe signatures of extreme event as intermittent extreme value amplitude of the dynamical variable in the nearest neighbors of dynamical units. The temporal dynamics of the dynamical units in the noncohrent subgroup separately does not reveal signature of the extreme events, however, local mean-field as a microscopic dynamics clearly shows large excursion from their average value that follows a log-tail Gaussian distribution.
To understand the mechanism of the coexisting extreme events, we took a simple two dynamical units' model of the Hindmarsh-Rose system under pure repulsive coupling which shows presence of extreme events. Two coupled bursting neurons establish antiphase (out-of-phase) synchronization when the repulsive coupling strength crosses a threshold. Near the threshold, the coupled dynamics shows intermittent jumps from the antiphase synchronization manifold as large excursions. The large excursion amplitudes in a long run of the dynamical variable show dragon-king [5] like probability distribution with a long tail. For a network of large number oscillators, the coherent subpopulation is in regular dynamical state while the noncoherent population is in a chaotic mode where the temporal dynamics of some of the oscillators intermittently jumps to large values. This is reflected as large excursion in their mean field dynamics that follows non-Gaussian statistics.
Acknowledgements
A.M. is supported by the University Grant Commission (UGC), India. S.S and S.K.D. are supported by the CSIR (India) Emeritus Scientist Scheme. S.K.D. also acknowledges support by the FAPESP (Grant No.2011/11973-4), Sao Paulo, Brazil and the Indo-Russian programme supported by DST-RFBR.
References
1. Y. Kuramoto, Battogtokh, Nonlin. Phen. Complex Syst 5, 380 (2002).
2. D.M. Abrams and S.H. Strogate, Phys.Rev.Letts. 93, 174102 (2004).
3. G. C. Sethia and A. Sen, Phys. Rev. Letts. 112, 144101 (2014).
4. A.Mishra, C.R.Hens, M.Bose, P.K.Roy, S.K.Dana, Phys. Rev. E 92, 062920 (2015); C. R. Hens, A.Mishra , P.K.Roy , A, Sen and S. K. Dana, Pramana -J. Phys. 84 (2), 229 (2015)
5. H.L. D. de S. Cavalcante, M. O., D. Sornette, E. Ott, D. J. Gauthier, Phys. Rev. Letts. 111, 198701 (2013).
6. A.Mishra, S. Saha, H. Cerdeira, S. K. Dana, (in preparation).
Semi-Analytical Approach to Criteria for Ignition of Excitation Waves
B. Bezekci, I. Idris, R. D. Simitev, V. N. Biktashev*
College of Engineering, Mathematics and Physical Sciences, University of Exeter. * Presenting e-mail: v.n.biktashev@exeter.ac.uk
We consider the problem of ignition of propagating waves in one-dimensional bistable or excitable systems by an
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36 Opera Med Physiol 2016 Vol. 2 (S1)
