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Asymptotic behavior of positive solutions of the equation $ \Delta u + K u^{\frac{n+2}{n-2}} = 0$ in $IR^n$ and positive scalar curvature
Synchronized and nonsymmetric phase-locked periodic solutions in a neteork of neurons with McCulloch-Pitts nonlinearity
| 1. | Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada, M3J lP3, Canada |
| [1] |
Jeremias Epperlein, Stefan Siegmund. Phase-locked trajectories for dynamical systems on graphs. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1827-1844. doi: 10.3934/dcdsb.2013.18.1827 |
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Seung-Yeal Ha, Jinyeong Park, Sang Woo Ryoo. Emergence of phase-locked states for the Winfree model in a large coupling regime. Discrete & Continuous Dynamical Systems - A, 2015, 35 (8) : 3417-3436. doi: 10.3934/dcds.2015.35.3417 |
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Ryotaro Tsuneki, Shinji Doi, Junko Inoue. Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators. Mathematical Biosciences & Engineering, 2014, 11 (1) : 125-138. doi: 10.3934/mbe.2014.11.125 |
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Guy Katriel. Stability of synchronized oscillations in networks of phase-oscillators. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 353-364. doi: 10.3934/dcdsb.2005.5.353 |
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Leszek Gasiński, Nikolaos S. Papageorgiou. Three nontrivial solutions for periodic problems with the $p$-Laplacian and a $p$-superlinear nonlinearity. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1421-1437. doi: 10.3934/cpaa.2009.8.1421 |
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Chiara Zanini, Fabio Zanolin. Periodic solutions for a class of second order ODEs with a Nagumo cubic type nonlinearity. Discrete & Continuous Dynamical Systems - A, 2012, 32 (11) : 4045-4067. doi: 10.3934/dcds.2012.32.4045 |
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Per Danzl, Ali Nabi, Jeff Moehlis. Charge-balanced spike timing control for phase models of spiking neurons. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1413-1435. doi: 10.3934/dcds.2010.28.1413 |
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Evgeny L. Korotyaev. Estimates for solutions of KDV on the phase space of periodic distributions in terms of action variables. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 219-225. doi: 10.3934/dcds.2011.30.219 |
| [9] |
Kota Kumazaki. Periodic solutions for non-isothermal phase transition models. Conference Publications, 2011, 2011 (Special) : 891-902. doi: 10.3934/proc.2011.2011.891 |
| [10] |
Raoul-Martin Memmesheimer, Marc Timme. Stable and unstable periodic orbits in complex networks of spiking neurons with delays. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1555-1588. doi: 10.3934/dcds.2010.28.1555 |
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Hongzi Cong, Jianjun Liu, Xiaoping Yuan. Quasi-periodic solutions for complex Ginzburg-Landau equation of nonlinearity $|u|^{2p}u$. Discrete & Continuous Dynamical Systems - S, 2010, 3 (4) : 579-600. doi: 10.3934/dcdss.2010.3.579 |
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Pablo Amster, Manuel Zamora. Periodic solutions for indefinite singular equations with singularities in the spatial variable and non-monotone nonlinearity. Discrete & Continuous Dynamical Systems - A, 2018, 38 (10) : 4819-4835. doi: 10.3934/dcds.2018211 |
| [13] |
Timothy J. Lewis. Phase-locking in electrically coupled non-leaky integrate-and-fire neurons. Conference Publications, 2003, 2003 (Special) : 554-562. doi: 10.3934/proc.2003.2003.554 |
| [14] |
Feng Zhang, Wei Zhang, Pan Meng, Jianzhong Su. Bifurcation analysis of bursting solutions of two Hindmarsh-Rose neurons with joint electrical and synaptic coupling. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 637-651. doi: 10.3934/dcdsb.2011.16.637 |
| [15] |
Ian Schindler, Kyril Tintarev. Mountain pass solutions to semilinear problems with critical nonlinearity. Conference Publications, 2007, 2007 (Special) : 912-919. doi: 10.3934/proc.2007.2007.912 |
| [16] |
Xianling Fan, Yuanzhang Zhao, Guifang Huang. Existence of solutions for the $p-$Laplacian with crossing nonlinearity. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 1019-1024. doi: 10.3934/dcds.2002.8.1019 |
| [17] |
Kyril Tintarev. Positive solutions of elliptic equations with a critical oscillatory nonlinearity. Conference Publications, 2007, 2007 (Special) : 974-981. doi: 10.3934/proc.2007.2007.974 |
| [18] |
Monica Musso, Donato Passaseo. Multiple solutions of Neumann elliptic problems with critical nonlinearity. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 301-320. doi: 10.3934/dcds.1999.5.301 |
| [19] |
Yan Zhang. Asymptotic behavior of a nonlocal KPP equation with an almost periodic nonlinearity. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 5183-5199. doi: 10.3934/dcds.2016025 |
| [20] |
Umberto Mosco. Impulsive motion on synchronized spatial temporal grids. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6069-6098. doi: 10.3934/dcds.2017261 |
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