Clustering, Communication and Environmental Oscillations in Populations of Budding Yeast, Chris Stowers, Brian Robertson, Hyunju Ban, Carl H. Johnson, T Young and Erik M. Boczko.
The Signed Distance Function: A New Tool for Binary Classification, with Erik Boczko.
Comparative Study of Sinc Collocation Method versus Hybrid Sinc-Finite Difference Methods for Solving Burgers' Equations, Moayad Odeh, Martin Mohlenkamp, Mohammed Usman, T Young, Engineering Letters , 33 (7) (2025) 2542-2556.
Instability of $k$-Cluster Solutions in a Cell Cycle Population Model when $k$ is Prime, Rabi K.C., Abdalnaser Algoud, T Young, J. Appl. Nonlin. Dynamics 11 (1) (2022) 87-138. doi: 10.5890/JAND.2022.03.007
Universality of Stable Multi-Cluster Periodic Solutions in a Population Model of the Cell Cycle with Negative Feedback, Kiattisak Prathom, T Young, J. Biolog. Dynamics 15 (2021), 455-522. doi: 10.1080/17513758.2021.1971781
Lyapunov Exponent, Liao Perturbation And Persistence, Wenxiang Sun, T Young, Sci.~China - Math. 63 2020, 1913-1928. doi: 10.1007/s11425-019-1660-5
Clusters Tend to be of Equal Size in a Negative Feedback Population Model of Cell Cycle Dynamics, Jan Rombouts, Kiattisak Prathom, T Young. SIAM J Appl Dynam Systems, 19 (2) 2020, 1540-1573. doi: 10.1137/19M129070X
Transient Dynamics of Block Coordinate Descent in a Valley, Martin Mohlenkamp, T Young, Balasz Barany. Intl J Num. Anal. Modeling 17 (4) 2020, 557-591.
Small Amplitude, Superimposed Horizontal Motion of a Load Supported Symmetrically by Rubber Springs, T Young, Millard F. Beatty. Math. & Mechanics of Solids 25 (3) 2020, 597-618. doi: 10.1177/1081286519885179
Instability of the Steady State Solution in Cell Cycle Population Structure Models with Feedback, Balasz Barany, Gregory Moses, T Young, J Math. Biology. 78 (5) 2019, 1365-1387. doi: 10.1007/s00285-018-1312-0
Temporal Clustering in Cell Cycle Dynamics, T Young, Kittisak Prathom, Jan Rombouts, Dynamical Systems Magazine, SIAM DSWeb, Jan 2019. Review article.
Coupling of the Cell Cycle and Metabolism in Yeast Cell-Cycle-Related Oscillations via Resource Criticality and Checkpoint Gating, Luke Morgan, Gregory Moses, T Young, Lett. BioMath. 5 (2018). doi: 10.1080/23737867.2018.1456366
The Optimization Landscape for Fitting a Rank-2 Tensor with a Rank-1 Tensor, Martin J Mohlenkamp, Xue Gong, T Young, SIAM J Appl Dyn Sys. 17 (2018), 1432-1477. doi: 10.1137/17M112213X
Early Treatment Gains for Antibiotic Administration and Within Human Host Time Series Data, Erik M Boczko, T Young, Math. Medicine & Biology 35 (2018), 203-224. doi:10.1093/imammb/dqw025
Two dimensional heteroclinic attractor in the generalized Lotka-Volterra system. Valentin S Afraimovich, Gregory Moses, T Young, Nonlinearity 29 (2016) 1645-1667. %ArXiv: 1509.04570. doi:10.1088/0951-7715/29/5/1645
Evidence for Internuclear Signaling in Drosophila Embryogenesis, Richard Buckalew, Kara Finley, Soichi Tanda, T Young, Developmental Dynamics 244 (2015), 1014-1021. doi: 10.1002/DVDY.24298
Cell Cycle Dynamics: Clustering is Universal in Negative Feedback Systems. Nathan Breitsch, Gregory Moses, Erik M Boczko, T Young, J Math Biology 70(5) (2015), 1151-1175. doi: 10.1007/s00285-014-0786-7
Hierarchical Heteroclinics In Dynamical Model Of Cognitive Processes: Chunking, Vlentian S Afraimovich, T Young, M Rabinovich, Intl. J. Bifur. Chaos 24 1450132 (2014). doi: 10.1142/S0218127414501326
Noise-induced dispersion and breakup of clusters in cell cycle dynamics, Xue Gong, Gregory Moses, Alexander Neiman, T Young, J Theor Biol. 335 (2014), 160-169. doi: j.jtbi.2014.03.034
Cell Cycle Feedback Model with a Gap, Xue Gong, Richard Buckalew, T Young, Erik M Boczko, J Biol. Dynamics 8 (2014), 79-98. dio:10.1080/17513758.2014.904526
Bifurcations of random differential equations with bounded noise, Ale Jan Homburg, T Young, M Gharaei, Chapter 9 in Bounded Noises in Physics, Biology & Engineering, A d'Onofrio ed., Birkhauser (2013). 137-154.
Two classes of ODE models with switch-like behavior, w/ Winfried Just, Mason Korb, Ben Elbert, Physica D 264 (2013), 35-48.
Sequential Dynamics of Master Slave Systems, Valentin S Afraimovich, Darius Cuevas, T Young, Dynam. Sys. 28 (2013), 154-172. doi: 10.1080/14689367.2010.522390
Non-Invasive detection of pulmonary pathogens in ventilator-circuit filters by PCR, RJ Isaacs, K Debelak, PR Norris, JM Jenkins, JC Rooks, T Young, Addison K May, Erik M Boczko, Amer J Translat Research 4(1) (2012), 72-82. PMC: 3276378
A Low Dimensional Dynamical Model of the Pulmonary Innate Immune Response to Infection, T Young, Richard Buckalew, Addison K May, Erik M Boczko, Math. Biosciences 235 (2012), 189-200. doi: 10.1016/j.mbs.2011.12.004. PMC: 3272130
The Hopf bifurcation with bounded noise, Ryan Botts, Ale Jan Homburg, T Young, Discrete Cont. Dynam. Systems - A 32 (2012), 2997-3007. doi:10.3934/dcds.2012.32.2997
Dynamics of a 3 cluster cell-cycle system with positive linear feedback, Bastien Fernandez, T Young, Technical report, Supplementary Material in J Theor. Biology 292 (2012). ArXiv: 1105.2803
Clustering in Cell Cycle Dynamics with General Responsive/Signaling Feedback, T Young, Bastien Fernandez, Richard Buckalew, Gregory Moses, Erik M Boczko, J Theor. Biology 292 (2012), 103-115. doi:10.1016/j.jtbi.2011.10.002. PMC: 3216642
Finite amplitude, horizontal motion of a load symmetrically supported between isotropic hyperelastic springs, Millard F Beatty, T Young. Intl J. Nonlin. Mechanics 47 (2012), 166-172. doi: 10.1016/ j.ijnonlinmec.2011.04.004
The Structure of Populations of Budding Yeast in Response to Feedback, CHris C Stowers, T Young and Erik M Boczko, Hypoth. Life Sciences 1(3) (2011), 71-84.
Nonlinear Dynamics of Emotion-Cognition Interaction: When Emotion Does not Destroy Cognition?, Valentin S Afraimovich, T Young, MK Muezzinoglu, M Rabinovich, Bull Math Biol., 73 (2011), 266-284.
ODE, RDE and SDE Models of Cell Cycle Dynamics and Clustering in Yeast, Erik M Boczko, Tomas Gedeon, Chris C Stowers and T Young, J Biological Dynamics 4 (2010), 328-345.
Stochastic Stability for Flows with Smooth Invariant Measures, Sergiu Aizicovici and TR Young, Libertas Matematica 30 (2010), 71-79.
Bifurcations for random differential equations with bounded noise on surfaces, by Ale Jan Homburg, T Young, Top. Meth. Nonlinear Analysis 35 (2010), 77-97.
Higher Order Birkhoff Averages, Thomas Jordan, Vincent Naudot and T Young, Dynamical Systems 24 (2009), 299-313.
Topological entropies for equivalent smooth flows, with Wenxiang Sun and Y.H. Zhou, Transactions of the American Mathematical Society 361 (2009), 3071-3082.
Convergence of Green Iterations for Schrodinger Equations, with Martin J. Mohlenkamp, Recent Advances in Computational Science, Jorgensen, P., Shen, X., Shu, C-W, and Yan, N., ed., World Scientific, 2008.
Jacobson's Theorem near saddle-node bifurcations, with Ale Jan Homburg, Discrete & Continuous Dyn. Systems 17 (2007), 21-58.
Hard bifurcations in dynamical systems with bounded random perturbations, with Ale Jan Homburg, Regular & Chaotic Dynamics 11 (2006), 247-258.
Binary Classification Based on Potential Functions,
with Erik Boczko and Andrew DiLullo,
Proc. Ohio Collaborative Conference on Bioinformatics, 2006.
Comparison of binary classification based on signed distance functions with support vector machines,
with Erik M Boczko, D. Wu and M.H. Xie,
Proc. Ohio Collaborative Conference on Bioinformatics, 2006.
Multipliers of homoclinic tangencies and
a theorem of Gonchenko and Shil'nikov on area preserving maps,
with Valentin S. Afraimovich,
Intl. J. Bif. Chaos 15 (2005), 3589-3594.
Critical saddle-node bifurcations and Morse-Smale maps,
with Brian Hunt,
Physica D 197 (2004), 1-17.
Basins of attraction for cascading maps, with Erik Boczko,
Intl. J. of Bifurcations and Chaos 14 (2004), 3557-3566.
A geometric proof of separatrix crossing results, with Shui-Nee Chow,
Nonlinear Analysis: Theory and Methods 56 (2004), 1047-1070.
Numerical observations of separatrix crossings, with Russell Francis,
Intl. J. of Bifurcations and Chaos 13 (2003), 511-520.
Existence of positive periodic solution for nonautonomous
preditor-prey system with diffusion and time delay,
with S.H. Chen and J.H. Zhang,
J. Computational Applied Math 159 (2003), 375-386.
Asymptotic measures and distributions of Birkhoff averages with respect to Lebesgue measure
Intermittency in families of unimodal maps
Universal scaling in homoclinic doubling cascades, with Ale Jan Homburg, Commun. Math. Physics 2 (2001) 2, 269-292.
Brikhoff averages and bifurcations, with Ale Jan Homburg, in Global Analysis of Dynamical Systems, Festchrift dedicated to Floris Takens for his 60th birthday. Eds. H. Broer, B. Krauskopf, G. Vegter. IOP publishing, Bristol, U.K., 2001.
Observed rotation numbers in families of circle maps, with MIcheal Saum, International J. Bifurcations and Chaos 11 (2001), 73-90.
Entropy and rotation intervals for circle maps near saddle-node bifurcations, Todd R Young Math. Zeit. 234 (2000), 487-506.
Multipliers of homoclinic orbits and characteristics of associated invariant sets, with Valentin S. Afraimovich, Discrete and Continuous Dynamical Systems 6 (2000), 691-704.
Mather invariants and smooth conjugacy on $S^2$, with Valentin S. Afraimovich, J. Dynam. Control Systems 6 (2000), 341-352.
Multipliers of heteroclinic orbits, with V. Afraimovich, Far East J. of Dyn. Systems 2 (2000), 41-51.
From Morse-Smale to all knots and links, with Robert Ghrist, Nonlinearity 11 (1998), 1111-1126.
Relative density of irrational rotation numbers in families of circle diffeomorphisms, with Valentina S. Afraimovich, Ergod. Th. Dyn. Systems 18 (1998), 1-16.
$C^k$ conjugacy of 1-d diffeomorphisms with fixed points, Todd R Young Proc. AMS 125 (1997), 1987-96.
Transition maps of homoclinic orbits and resonances near bifurcations of circle maps, Todd R Young in Hamiltonian Dynamics and Celestial Mechanics, Contemp. Math. 198, eds. D. Saari & Z. Xia, 1996.
Conventional multipliers for homoclinic orbits, with Valentin S. Afraimovich, WeiShi Liu, Nonlinearity 9 (1996), 115-136.
$C^{k}$-smoothness of invariant curves in a global saddle-node bifurcation, Todd R Young Journal of Differential Equations 126 (1996), 62-86.
A result in global bifurcation theory using the Conley index, Todd R Young Discrete and Continuous Dynamical Systems 2 (1996), 387-396.
Partially hyperbolic sets from a co-dimension one bifurcation, Todd R Young Discrete and Continuous Dynamical Systems 1 (1995), 253-275.
One-step discretizations of differential equations: transversality, and nonlocal bifurcations, Todd R Young Dynamic Systems and Applications 4 (1995), 237-249.
Generalization of a theorem of Malta and Palis, with Valentin S. Afraimovich, in Dynamical Systems and Applications, WSSIAA 4 1995, 11-25.