Preprints

All files are Postscript or PDF, compressed with gzip

Clustering, Communication and Environmental Oscillations in Populations of Budding Yeast, Chris Stowers, Brian Robertson, Hyunju Ban, Carl H. Johnson, Todd Young and Erik M. Boczko.

Nonlinear dynamics of mental processes: Emotion-cognition interaction, by V.~Afraimovich, T.~Young, M.K.~Muezzinoglu, M.~Rabinovich, submitted 3/09.

ODE, RDE and SDE Models of Cell Cycle Dynamics and Clustering in Yeast, Erik M. Boczko, Tomas Gedeon, Chris C. Stowers and Todd Young, to appear in the Journal of Biological Dynamics.

Higher Order Birkhoff Averages, with Thomas Jordan and Vincent Naudot, to appear in Dynamical Systems.

The Signed Distance Function: A New Tool for Binary Classification, with Erik Boczko.

Liao Standard Systems and Nonzero Lyapunov Exponents for Differential Flows, with Wenxiang Sun.

Publications

Topological entropies for equivalent smooth flows, , with W.X.~Sun and Y.H.~Zhou, Transactions of the American Mathematical Society 361 (2009), 3071-3082.

Convergence of Green Iterations for Schr\"{o}dinger Equations, with M.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 A.J. 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 E.~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 V.~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, Discrete and Continuous Dynamical Systems 9 (2003), 359-378.

Intermittency in families of unimodal maps, with A.J. Homburg, Ergod. Th. Dyn. Systems 22 (2002), 203-225.

Universal scaling in homoclinic doubling cascades, with A. J. 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 M. Saum, International J. Bifurcations and Chaos 11 (2001), 73-90.

Entropy and rotation intervals for circle maps near saddle-node bifurcations, Math. Zeit. 234 (2000), 487-506.

Multipliers of homoclinic orbits and characteristics of associated invariant sets, with V. Afraimovich, Discrete and Continuous Dynamical Systems 6 (2000), 691-704.

Mather invariants and smooth conjugacy on $S^2$, with V. 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 R. Ghrist, Nonlinearity 11 (1998), 1111-1126.

Relative density of irrational rotation numbers in families of circle diffeomorphisms, with V. Afraimovich, Ergod. Th. Dyn. Systems 18 (1998), 1-16.

$C^k$ conjugacy of 1-d diffeomorphisms with fixed points, Proc. AMS 125 (1997), 1987-96.

Transition maps of homoclinic orbits and resonances near bifurcations of circle maps, in Hamiltonian Dynamics and Celestial Mechanics, Contemp. Math. 198, eds. D. Saari & Z. Xia, 1996.

Conventional multipliers for homoclinic orbits, with V. Afraimovich, W.-S. Liu, Nonlinearity 9 (1996), 115-136.

$C^{k}$-smoothness of invariant curves in a global saddle-node bifurcation, Journal of Differential Equations 126 (1996), 62-86.

A result in global bifurcation theory using the Conley index, Discrete and Continuous Dynamical Systems 2 (1996), 387-396.

Partially hyperbolic sets from a co-dimension one bifurcation, Discrete and Continuous Dynamical Systems 1 (1995), 253-275.

One-step discretizations of differential equations: transversality, and nonlocal bifurcations, Dynamic Systems and Applications 4 (1995), 237-249.

Generalization of a theorem of Malta and Palis, with V. Afraimovich, in Dynamical Systems and Applications, WSSIAA 4 1995, 11-25.


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