In neuronal models of bifurcation type 2 (Chapter 14), the possibility of stable rest is abolished via a Hopf bifurcation as I rises above Ic, and the possibility of stable periodic firing is abolished via a collision of the stable limit cycle with an unstable periodic orbit as I falls below I∗, with I∗ < Ic. In neuronal models of bifurcation type 1 (Chapter 12), there is no distinction between I∗ and Ic; stable rest is abolished as I rises above Ic, and stable periodic firing is abolished as I falls below Ic.
Hopf Bifurcation Model Neuron Sodium Current Stable Limit Cycle Stable Node
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I. Alekseichuk, Z. Turi, G. A. de Lara, A. Antal, and W. Paulus, Spatial working memory in humans depends on theta and high gamma synchronization in the prefrontal cortex, Current Biology, 26 (2016), pp. 1513–1521.CrossRefGoogle Scholar
W. E. Crill, Persistent sodium current in mammalian central neurons, Ann. Rev. Physiol., 58 (1996), pp. 349–362.CrossRefGoogle Scholar
E. M. Izhikevich,,, Dynamical Systems in Neuroscience, MIT Press, 2007.Google Scholar
M. Leszczyński, J. Fell, and N. Axmacher, Rhythmic working memory activation in the human hippocampus, Cell Reports, 13 (2015), pp. 1272–1282.CrossRefGoogle Scholar
C. E. Stafstrom, Persistent sodium current and its role in epilepsy, Epilepsy Curr., 7 (2007), pp. 15–22.CrossRefGoogle Scholar
S. H. Strogatz, Nonlinear Dynamics and Chaos, Westview Press, 2nd ed., 2015.Google Scholar
M. Wang, Y. Yang, C.-J. Wang, N. J. Gamo, L. E. Jin, J. A. Mazer, J. H. Morrison, X.-J. Wang, and A. F. T. Arnsten, NMDA receptors subserve persistent neuronal firing during working memory in dorsolateral prefrontal cortex, Neuron, 77 (2013), pp. 736–749.CrossRefGoogle Scholar
J. Yamamoto, J. Suh, D. Takeuchi, and S. Tonegawa, Successful execution of working memory linked to synchronized high-frequency gamma oscillations, Cell, 157 (2014), pp. 845–857.CrossRefGoogle Scholar