Discontinuity-induced bifurcation cascades in flows and maps with application to models of the yeast cell cycle

di Bernardo, 2008 Li, 2010, A mathematical model for cell size control in fission yeast, J. Theoret. Biol., 264, 771, 10.1016/j.jtbi.2010.03.023 Pfeuty, 2007, Minimal requirements for robust cell size control in eukaryotic cells, Physical Biol., 4, 194, 10.1088/1478-3975/4/3/006 Tyson, 2010, Cell cycle controls Qu, 2003, Dynamics of the cell cycle: checkpoints, sizers, and timers, Biophys. J., 85, 3600, 10.1016/S0006-3495(03)74778-X Noel, 2011, Algorithm for identification of piecewise smooth hybrid systems: application to eukaryotic cell cycle regulation, vol. 6833, 225 Alfieri, 2011, Modeling the cell cycle: from deterministic models to hybrid systems, BioSystems, 105, 34, 10.1016/j.biosystems.2011.03.002 Hogan, 2007, Dynamics of a piecewise linear map with a gap, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 463, 49, 10.1098/rspa.2006.1735 Dutta, 2008, On the existence of low-period orbits in n-dimensional piecewise linear discontinuous maps, Nonlinear Dynam., 53, 369, 10.1007/s11071-007-9318-y Rajpathak, 2012, Analysis of stable periodic orbits in the one dimensional linear piecewise-smooth discontinuous map, Chaos, 22, 033126, 10.1063/1.4740061 Glendinning, 1993, The anharmonic route to chaos: kneading theory, Nonlinearity, 6, 349, 10.1088/0951-7715/6/3/001 Keener, 1980, Chaotic behavior in piecewise continuous difference-equations, Trans. Amer. Math. Soc., 261, 589, 10.1090/S0002-9947-1980-0580905-3 Dias De Deus, 1987, Scaling behaviour of windows and intermittency in one-dimensional maps, Phys. Lett. A, 124, 433, 10.1016/0375-9601(87)90547-0 Mosekilde, 2001, Bifurcation structure of a model of bursting pancreatic cells, BioSystems, 63, 3, 10.1016/S0303-2647(01)00142-3 Budd, 2006, Corner bifurcations in non-smoothly forced impact oscillators, Physica D, 220, 127, 10.1016/j.physd.2006.07.001 Dankowicz, 2013 Dankowicz, 2012, Discontinuity-induced bifurcations in models of mechanical contact, capillary adhesion, and cell division: a common framework, Physica D, 241, 1869, 10.1016/j.physd.2011.05.001 Dutta, 2010, Period increment cascades in a discontinuous map with square-root singularity, Discrete Contin. Dyn. Syst. Ser. B, 14, 961, 10.3934/dcdsb.2010.14.961 Pring, 2011, The dynamics of a simplified pinball machine, IMA J. Appl. Math., 76, 67, 10.1093/imamat/hxq064 Duarte, 2012, Scaling law in saddle–node bifurcations for one-dimensional maps: a complex variable approach, Nonlinear Dynam., 67, 541, 10.1007/s11071-011-0004-8 Rakshit, 2010, Bifurcation phenomena in two-dimensional piecewise smooth discontinuous maps, Chaos, 20, 033101, 10.1063/1.3422475 Gérard, 2010, From simple to complex patterns of oscillatory behavior in a model for the mammalian cell cycle containing multiple oscillatory circuits, Chaos, 20, 045109, 10.1063/1.3527998 Marshall, 2012, What determines cell size?, BMC Biol., 10, 101, 10.1186/1741-7007-10-101 Turner, 2012, Cell size control in yeast, Current Biology, 22, R350, 10.1016/j.cub.2012.02.041 Hoose, 2012, A systematic analysis of cell cycle regulators in yeast reveals that most factors act independently of cell size to control initiation of division, PLoS Genetics, 8, e1002590, 10.1371/journal.pgen.1002590 Avrutin, 2007, Codimension-three bifurcations: explanation of the complex one-, two-, and three-dimensional bifurcation structures in nonsmooth maps, Phys. Rev. E (3), 75, 066205, 10.1103/PhysRevE.75.066205 Avrutin, 2011, Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps, Nonlinearity, 24, 2575, 10.1088/0951-7715/24/9/012 Avrutin, 2010, Calculation of bifurcation curves by map replacement, Int. J. Bifurcation Chaos, 20, 3105, 10.1142/S0218127410027581 Gardini, 2010, Border-collision bifurcations in 1d piecewise-linear maps and leonov’s approach, Int. J. Bifurcation Chaos, 20, 3085, 10.1142/S021812741002757X Gardini, 2011, Critical homoclinic orbits lead to snap-back repellers, Chaos Solitons Fractals, 44, 433, 10.1016/j.chaos.2011.03.004 Yamaguchi, 1996, The order of appearance of oscillation modes of a piecewise linear map, J. Phys. Soc. Japan, 65, 3500, 10.1143/JPSJ.65.3500