Duchet, Benoit; Weerasinghe, Gihan; Cagnan, Hayriye; Brown, Peter; Bick, Christian; Bogacz, Rafal Phase-dependence of response curves to deep brain stimulation and their relationship: from essential tremor patient data to a Wilson-Cowan model. (English) Zbl 1443.92047 J. Math. Neurosci. 10, Paper No. 4, 39 p. (2020). MSC: 92B20 92C50 92C20 PDF BibTeX XML Cite \textit{B. Duchet} et al., J. Math. Neurosci. 10, Paper No. 4, 39 p. (2020; Zbl 1443.92047) Full Text: DOI
Chartrand, Thomas; Goldman, Mark S.; Lewis, Timothy J. Synchronization of electrically coupled resonate-and-fire neurons. (English) Zbl 1429.92033 SIAM J. Appl. Dyn. Syst. 18, No. 3, 1643-1693 (2019). MSC: 92B25 92C20 34D06 34C15 PDF BibTeX XML Cite \textit{T. Chartrand} et al., SIAM J. Appl. Dyn. Syst. 18, No. 3, 1643--1693 (2019; Zbl 1429.92033) Full Text: DOI Link arXiv
Hesse, Janina; Schreiber, Susanne How to correctly quantify neuronal phase-response curves from noisy recordings. (English) Zbl 1427.92026 J. Comput. Neurosci. 47, No. 1, 17-30 (2019). MSC: 92C20 PDF BibTeX XML Cite \textit{J. Hesse} and \textit{S. Schreiber}, J. Comput. Neurosci. 47, No. 1, 17--30 (2019; Zbl 1427.92026) Full Text: DOI
Abel, John H.; Chakrabarty, Ankush; Klerman, Elizabeth B.; Doyle, Francis J. Pharmaceutical-based entrainment of circadian phase via nonlinear model predictive control. (English) Zbl 1415.92030 Automatica 100, 336-348 (2019). MSC: 92B25 92C50 92C42 93B40 93B52 PDF BibTeX XML Cite \textit{J. H. Abel} et al., Automatica 100, 336--348 (2019; Zbl 1415.92030) Full Text: DOI
Adrian, Daniel W.; Maitra, Ranjan; Rowe, Daniel B. Complex-valued time series modeling for improved activation detection in fMRI studies. (English) Zbl 1405.62152 Ann. Appl. Stat. 12, No. 3, 1451-1478 (2018). MSC: 62P10 62M10 62J10 PDF BibTeX XML Cite \textit{D. W. Adrian} et al., Ann. Appl. Stat. 12, No. 3, 1451--1478 (2018; Zbl 1405.62152) Full Text: DOI Euclid
Akcay, Zeynep; Huang, Xinxian; Nadim, Farzan; Bose, Amitabha Phase-locking and bistability in neuronal networks with synaptic depression. (English) Zbl 1380.34055 Physica D 364, 8-21 (2018). MSC: 34C15 92B20 37N25 PDF BibTeX XML Cite \textit{Z. Akcay} et al., Physica D 364, 8--21 (2018; Zbl 1380.34055) Full Text: DOI
Dodla, Ramana; Wilson, Charles J. Effect of phase response curve shape and synaptic driving force on synchronization of coupled neuronal oscillators. (English) Zbl 1414.92064 Neural Comput. 29, No. 7, 1769-1814 (2017). MSC: 92B25 92C20 PDF BibTeX XML Cite \textit{R. Dodla} and \textit{C. J. Wilson}, Neural Comput. 29, No. 7, 1769--1814 (2017; Zbl 1414.92064) Full Text: DOI
Núñez, Felipe; Wang, Yongqiang; Teel, Andrew R.; Doyle, Francis J. III Synchronization of pulse-coupled oscillators to a global pacemaker. (English) Zbl 1336.93022 Syst. Control Lett. 88, 75-80 (2016). MSC: 93A14 93C95 34C15 PDF BibTeX XML Cite \textit{F. Núñez} et al., Syst. Control Lett. 88, 75--80 (2016; Zbl 1336.93022) Full Text: DOI
Efimov, D. Phase resetting for a network of oscillators via phase response curve approach. (English) Zbl 1344.92063 Biol. Cybern. 109, No. 1, 95-108 (2015). MSC: 92C42 92B25 PDF BibTeX XML Cite \textit{D. Efimov}, Biol. Cybern. 109, No. 1, 95--108 (2015; Zbl 1344.92063) Full Text: DOI
Ohara, Takayuki; Fukuda, Hirokazu; Tokuda, Isao T. An extended mathematical model for reproducing the phase response of Arabidopsis thaliana under various light conditions. (English) Zbl 1343.92035 J. Theor. Biol. 382, 337-344 (2015). MSC: 92B25 92C80 PDF BibTeX XML Cite \textit{T. Ohara} et al., J. Theor. Biol. 382, 337--344 (2015; Zbl 1343.92035) Full Text: DOI
Verduzco-Flores, Sergio Stochastic synchronization in purkinje cells with feedforward inhibition could be studied with equivalent phase-response curves. (English) Zbl 1357.92017 J. Math. Neurosci. 5, Paper No. 13, 32 p. (2015). MSC: 92C20 PDF BibTeX XML Cite \textit{S. Verduzco-Flores}, J. Math. Neurosci. 5, Paper No. 13, 32 p. (2015; Zbl 1357.92017) Full Text: DOI
Núñez, Felipe; Wang, Yongqiang; Doyle, Francis Joseph III Global synchronization of pulse-coupled oscillators interacting on cycle graphs. (English) Zbl 1309.93075 Automatica 52, 202-209 (2015). MSC: 93C15 94C15 PDF BibTeX XML Cite \textit{F. Núñez} et al., Automatica 52, 202--209 (2015; Zbl 1309.93075) Full Text: DOI
Dasanayake, Isuru S.; Li, Shin jun. Constrained charge-balanced minimum-power controls for spiking neuron oscillators. (English) Zbl 1305.49023 Syst. Control Lett. 75, 124-130 (2015). MSC: 49K15 34H05 PDF BibTeX XML Cite \textit{I. S. Dasanayake} and \textit{S. Li jun.}, Syst. Control Lett. 75, 124--130 (2015; Zbl 1305.49023) Full Text: DOI arXiv
Akcay, Zeynep; Bose, Amitabha; Nadim, Farzan Effects of synaptic plasticity on phase and period locking in a network of two oscillatory neurons. (English) Zbl 1291.92019 J. Math. Neurosci. 4, Paper No. 8, 29 p. (2014). MSC: 92C20 PDF BibTeX XML Cite \textit{Z. Akcay} et al., J. Math. Neurosci. 4, Paper No. 8, 29 p. (2014; Zbl 1291.92019) Full Text: DOI
Moehlis, Jeff Improving the precision of noisy oscillators. (English) Zbl 1288.34052 Physica D 272, 8-17 (2014). MSC: 34F05 34C15 34C25 PDF BibTeX XML Cite \textit{J. Moehlis}, Physica D 272, 8--17 (2014; Zbl 1288.34052) Full Text: DOI
Dodla, Ramana; Wilson, Charles J. Effect of phase response curve skewness on synchronization of electrically coupled neuronal oscillators. (English) Zbl 1415.92031 Neural Comput. 25, No. 10, 2545-2610 (2013). MSC: 92B25 92C20 PDF BibTeX XML Cite \textit{R. Dodla} and \textit{C. J. Wilson}, Neural Comput. 25, No. 10, 2545--2610 (2013; Zbl 1415.92031) Full Text: DOI
Dodla, Ramana; Wilson, Charles J. Spike width and frequency alter stability of phase-locking in electrically coupled neurons. (English) Zbl 1267.92021 Biol. Cybern. 107, No. 3, 367-383 (2013). MSC: 92C20 92C05 92B25 92B20 PDF BibTeX XML Cite \textit{R. Dodla} and \textit{C. J. Wilson}, Biol. Cybern. 107, No. 3, 367--383 (2013; Zbl 1267.92021) Full Text: DOI
Lin, Kevin K.; Wedgwood, Kyle C. A.; Coombes, Stephen; Young, Lai-Sang Limitations of perturbative techniques in the analysis of rhythms and oscillations. (English) Zbl 1256.92006 J. Math. Biol. 66, No. 1-2, 139-161 (2013). MSC: 92B25 37N25 92C20 65C20 PDF BibTeX XML Cite \textit{K. K. Lin} et al., J. Math. Biol. 66, No. 1--2, 139--161 (2013; Zbl 1256.92006) Full Text: DOI
Fujita, Tomohiro; Fukai, Tomoki; Kitano, Katsunori Influences of membrane properties on phase response curve and synchronization stability in a model globus pallidus neuron. (English) Zbl 1446.92045 J. Comput. Neurosci. 32, No. 3, 539-553 (2012). MSC: 92B20 92C20 92B25 PDF BibTeX XML Cite \textit{T. Fujita} et al., J. Comput. Neurosci. 32, No. 3, 539--553 (2012; Zbl 1446.92045)
Lücken, Leonhard; Yanchuk, Serhiy Two-cluster bifurcations in systems of globally pulse-coupled oscillators. (English) Zbl 1252.34042 Physica D 241, No. 4, 350-359 (2012). Reviewer: Oleksandr Popovych (Jülich) MSC: 34C15 34D06 34D20 34C23 34D10 PDF BibTeX XML Cite \textit{L. Lücken} and \textit{S. Yanchuk}, Physica D 241, No. 4, 350--359 (2012; Zbl 1252.34042) Full Text: DOI
Maran, Selva K.; Sieling, Fred H.; Demla, Kavita; Prinz, Astrid A.; Canavier, Carmen C. Responses of a bursting pacemaker to excitation reveal spatial segregation between bursting and spiking mechanisms. (English) Zbl 1446.92062 J. Comput. Neurosci. 31, No. 2, 419-440 (2011). MSC: 92B20 92B25 PDF BibTeX XML Cite \textit{S. K. Maran} et al., J. Comput. Neurosci. 31, No. 2, 419--440 (2011; Zbl 1446.92062)
Oh, Myongkeun; Matveev, Victor Non-weak inhibition and phase resetting at negative values of phase in cells with fast-slow dynamics at hyperpolarized potentials. (English) Zbl 1446.92159 J. Comput. Neurosci. 31, No. 1, 31-42 (2011). MSC: 92C20 PDF BibTeX XML Cite \textit{M. Oh} and \textit{V. Matveev}, J. Comput. Neurosci. 31, No. 1, 31--42 (2011; Zbl 1446.92159)
Proctor, J.; Kukillaya, R. P.; Holmes, P. A phase-reduced neuro-mechanical model for insect locomotion: feed-forward stability and proprioceptive feedback. (English) Zbl 1211.93099 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 368, No. 1930, 5087-5104 (2010). MSC: 93C95 92C20 34C29 93B52 PDF BibTeX XML Cite \textit{J. Proctor} et al., Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 368, No. 1930, 5087--5104 (2010; Zbl 1211.93099) Full Text: DOI
Osinga, Hinke M.; Moehlis, Jeff Continuation-based computation of global isochrons. (English) Zbl 1232.37014 SIAM J. Appl. Dyn. Syst. 9, No. 4, 1201-1228 (2010). MSC: 37C10 65P99 37N25 PDF BibTeX XML Cite \textit{H. M. Osinga} and \textit{J. Moehlis}, SIAM J. Appl. Dyn. Syst. 9, No. 4, 1201--1228 (2010; Zbl 1232.37014) Full Text: DOI
Goldwyn, Eli E.; Hastings, Alan Small heterogeneity has large effects on synchronization of ecological oscillators. (English) Zbl 1169.92044 Bull. Math. Biol. 71, No. 1, 130-144 (2009). MSC: 92D40 37N25 PDF BibTeX XML Cite \textit{E. E. Goldwyn} and \textit{A. Hastings}, Bull. Math. Biol. 71, No. 1, 130--144 (2009; Zbl 1169.92044) Full Text: DOI
Goldwyn, Eli E.; Hastings, Alan When can dispersal synchronize populations? (English) Zbl 1210.92051 Theor. Popul. Biol. 73, No. 3, 395-402 (2008). MSC: 92D40 37N25 PDF BibTeX XML Cite \textit{E. E. Goldwyn} and \textit{A. Hastings}, Theor. Popul. Biol. 73, No. 3, 395--402 (2008; Zbl 1210.92051) Full Text: DOI
Tang, Sanyi A comparison investigation of the simplest models of circadian rhythms. (English) Zbl 1155.92012 Int. J. Biomath. 1, No. 1, 75-93 (2008). MSC: 92C30 34K20 34K60 92C37 34K18 PDF BibTeX XML Cite \textit{S. Tang}, Int. J. Biomath. 1, No. 1, 75--93 (2008; Zbl 1155.92012) Full Text: DOI
Troyer, Todd W. Factors affecting phase synchronization in integrate-and-fire oscillators. (English) Zbl 1119.92021 J. Comput. Neurosci. 20, No. 2, 191-200 (2006). MSC: 92C20 92C05 PDF BibTeX XML Cite \textit{T. W. Troyer}, J. Comput. Neurosci. 20, No. 2, 191--200 (2006; Zbl 1119.92021) Full Text: DOI
Forger, Daniel B.; Peskin, Charles S. Model based conjectures on mammalian clock controversies. (English) Zbl 1447.92008 J. Theor. Biol. 230, No. 4, 533-539 (2004). MSC: 92B25 PDF BibTeX XML Cite \textit{D. B. Forger} and \textit{C. S. Peskin}, J. Theor. Biol. 230, No. 4, 533--539 (2004; Zbl 1447.92008) Full Text: DOI
Ramírez Ávila, G. M.; Guisset, J. L.; Deneubourg, J. L. Synchronization in light-controlled oscillators. (English) Zbl 1034.81556 Physica D 182, No. 3-4, 254-273 (2003). MSC: 81V80 81-05 81-04 PDF BibTeX XML Cite \textit{G. M. Ramírez Ávila} et al., Physica D 182, No. 3--4, 254--273 (2003; Zbl 1034.81556) Full Text: DOI
Goel, Pranay; Ermentrout, Bard Synchrony, stability, and firing patterns in pulse-coupled oscillators. (English) Zbl 1008.70017 Physica D 163, No. 3-4, 191-216 (2002). MSC: 70K99 92B20 PDF BibTeX XML Cite \textit{P. Goel} and \textit{B. Ermentrout}, Physica D 163, No. 3--4, 191--216 (2002; Zbl 1008.70017) Full Text: DOI
Canavier, C. C.; Baxter, D. A.; Clark, J. W.; Byrne, J. H. Control of multistability in ring circuits of oscillators. (English) Zbl 0918.92008 Biol. Cybern. 80, No. 2, 87-102 (1999). MSC: 92C20 92B20 PDF BibTeX XML Cite \textit{C. C. Canavier} et al., Biol. Cybern. 80, No. 2, 87--102 (1999; Zbl 0918.92008) Full Text: DOI
Seidel, H.; Herzel, H. Bifurcations in a nonlinear model of the baroreceptor-cardiac reflex. (English) Zbl 0932.92024 Physica D 115, No. 1-2, 145-160 (1998). MSC: 92C50 92C30 PDF BibTeX XML Cite \textit{H. Seidel} and \textit{H. Herzel}, Physica D 115, No. 1--2, 145--160 (1998; Zbl 0932.92024) Full Text: DOI
Abramovich-Sivan, Sarit; Akselrod, Solange A pacemaker cell pair model based on the phase response curve. (English) Zbl 0938.92008 Biol. Cybern. 79, No. 1, 77-86 (1998). MSC: 92C30 PDF BibTeX XML Cite \textit{S. Abramovich-Sivan} and \textit{S. Akselrod}, Biol. Cybern. 79, No. 1, 77--86 (1998; Zbl 0938.92008) Full Text: DOI
Abramovich-Sivan, Sarit; Akselrod, Solange A single pacemaker cell model based on the phase response curve. (English) Zbl 0938.92007 Biol. Cybern. 79, No. 1, 67-76 (1998). MSC: 92C30 PDF BibTeX XML Cite \textit{S. Abramovich-Sivan} and \textit{S. Akselrod}, Biol. Cybern. 79, No. 1, 67--76 (1998; Zbl 0938.92007) Full Text: DOI
Canavier, C. C.; Butera, R. J.; Dror, R. O.; Baxter, D. A.; Clark, J. W.; Byrne, J. H. Phase response characteristics of model neurons determine which patterns are expressed in a ring circuit model of gait generation. (English) Zbl 0901.92011 Biol. Cybern. 77, No. 6, 367-380 (1997). MSC: 92C20 92B20 PDF BibTeX XML Cite \textit{C. C. Canavier} et al., Biol. Cybern. 77, No. 6, 367--380 (1997; Zbl 0901.92011) Full Text: DOI
Herrmann, K.; Mihovsky, I. M. Plastic behaviour of fibre-reinforced composites and fracture effects. (English) Zbl 0549.73060 Rozpr. Inż. 31, 165-177 (1983). MSC: 74E30 74R05 74R20 PDF BibTeX XML Cite \textit{K. Herrmann} and \textit{I. M. Mihovsky}, Rozpr. Inż. 31, 165--177 (1983; Zbl 0549.73060)
Suzuki, Ryoji; Kawato, Mitsuo; Tatsumi, Hitoshi Mathematical and phenomenological studies of biological rhythms. (English) Zbl 0527.92003 Cybernetics and systems research, Proc. 6th Eur. Meet., Vienna/ Austria 1982, 327-331 (1982). MSC: 92B05 92F05 92Cxx PDF BibTeX XML
Ikeda, Noriaki Model of bidirectional interaction between myocardial pacemakers based on the phase response curve. (English) Zbl 0503.92004 Biol. Cybern. 43, 157-167 (1982). MSC: 92Cxx 39A10 PDF BibTeX XML Cite \textit{N. Ikeda}, Biol. Cybern. 43, 157--167 (1982; Zbl 0503.92004) Full Text: DOI
Tao, K. M.; Zunde, P. On Levy’s identification, its generalization and applications. (English) Zbl 0471.93025 Int. J. Syst. Sci. 12, 1317-1334 (1981). MSC: 93B30 93B40 93B35 93E11 PDF BibTeX XML Cite \textit{K. M. Tao} and \textit{P. Zunde}, Int. J. Syst. Sci. 12, 1317--1334 (1981; Zbl 0471.93025) Full Text: DOI