McGill.CA / Mathematical Physiology Laboratory / Publications

1990 - 1999

  • 1990: M.C. Mackey & J.G. Milton. "A deterministic approach to survival statistics", J. Math. Biol. (1990) 28, 33-48. pdf file
  • 1990: M.C. Mackey & J. Milton. "Feedback, delays, and the origins of blood cell dynamics", Comm. on Theor. Biol. (1990) 1, 299-327. mackey-milton-1990.pdf
  • 1990: M.C. Mackey, A. Longtin, & A. Lasota. "Noise induced global asymptotic stability", J. Stat. Phys. (1990), 60, 735-751. pdf file
  • 1990: A. Longtin, J.G. Milton, J.E. Bos & M.C. Mackey. "Noise and critical behaviour of the pupil light reflex at oscillation onset'', Phys. Rev. A. (1990), 41, 6992-7005. pdf file
  • 1990: J.G. Milton, U. an der Heiden, A. Longtin, & M.C. Mackey. "Complex dynamics and noise in simple neural networks with delayed mixed feedback", Biomed. Biochim. Acta (1990). 49, 697-707.  pdf file
  • 1990: U. an der Heiden, A. Longtin, M.C. Mackey, J.G. Milton, & R. Scholl. "Oscillatory modes in a nonlinear second order differential equation with delay", J. Dynam. & Diff. Eqns. (1990), 2, 423-449. pdf file
  • 1990: J. Losson, M.C. Mackey & C. Cortis.  "Analog simulation of delayed dynamics:  Bifurcations and chaos." Proc. Ann. Conf. IEEE Engineering in Medicine and Biology Society (1990), 12, 989-991. pdf file
  • 1991: A. Lasota, K. Loskot, & M.C. Mackey. "Stability properties of proliferatively coupled cell replication models", Acta Biotheor. (1991), 39, 1-14. pdf file
  • 1991: N. Provatas & M.C. Mackey. "Noise induced asymptotic periodicity in a piecewise linear map." J. Stat. Phys. (1991), 63, 661-688. pdf file
  • 1991: M.C. Mackey. "The second law of thermodynamics: Comments from ergodic theory", in Nonlinear Fields: Classical, Random, Semiclassical (eds. P. Garbaczewski & Z. Popowicz), [Proceedings of the XXVII Karpacz Winter School in Theoretical Physics], World Scientific, 1991, pp. 384-415.PDF icon karpacz.pdf
  • 1991: N. Provatas & M.C. Mackey. "Asymptotic periodicity and banded chaos." Physica D (1991), 53, 295-318. pdf file
  • 1992: A. Rey & M.C. Mackey. "Bifurcations and traveling waves in a delayed partial differential equation", Chaos (1992), 2, 231-244. pdf file
  • 1992: J. Losson & M.C. Mackey. "A Hopf-like equation and perturbation theory for differential delay equations", J. Stat. Phys. (1992), 69, 1025-1046. pdf file
  • 1992: A. Lasota, M.C. Mackey, & J. Tyrcha. "The statistical dynamics of recurrent biological events", J. Math. Biol. (1992), 30, 775-800. pdf file
  • 1993: A. Rey & M.C. Mackey. "Multistability and boundary layer development in a transport equation with delayed arguments", Can. Appl. Math. Quar. (1993), 1, 1-21.PDF icon rey-mcm-1993.pdf
  • 1993: M.C. Mackey & H. Schwegler. "Ensemble and trajectory statistics in a nonlinear partial differential equation", J. Stat. Phys. (1993), 70, 281-295. pdf file
  • 1993: J. Losson, M.C. Mackey, & A. Longtin. "Solution multistability in first order nonlinear differential delay equations", Chaos (1993), 3, 167-176. pdf file
  • 1994: H. Schwegler & M.C. Mackey. "A Simple Model for the Approach of Entropy to Thermodynamic Equilibrium", J. Phys. A: Math. Gen. (1994), 27, 1939-1951. pdf file
  • 1994: J. Losson & M.C. Mackey. "Coupling induced statistical cycling in two diffusively coupled maps", Physica D (1994), 72, 324-342. pdf file
  • 1994: M.C. Mackey & I. Nechayeva. "Noise and stability in differential delay equations", J. Dynam. & Diff. Eqns. (1994), 6, 395-426. pdf file
  • 1994: M.O. Vlad, M.C. Mackey & J. Ross. "A generating functional approach to space and time dependent colored noise", Phys. Rev. E. (1994), 50, 798-821. pdf file
  • 1994: J. Losson & M.C. Mackey. "Statistical cycling in coupled map lattices", Phys. Rev. E. (1994), 50, 843-856.pdf file
  • 1994: R. Rudnicki & M.C. Mackey. "Asymptotic similarity and Malthusian growth in autonomous and nonautonomous populations", J. Math. Anal. Applic. (1994), 187, 548-566. pdf file
  • 1994: H. Schwegler & M.C. Mackey. "Fluctuations in circulating cell numbers following chemotherapy or bone marrow transplant", J. Math. Biol. (1994) 32, 761-770. pdf file
  • 1994: M.O. Vlad & M.C. Mackey. "Multiple logarithmic oscillations for statistical fractals on ultrametric spaces with application to recycle flows in hierarchial porous media", Physica Scripta (1994) 50, 615-623.  vlad-mackey-1994-log.pdf
  • 1994: M.C. Mackey & R. Rudnicki. "Global stability in a delayed partial differential equation describing cellular replication", J. Math. Biol. (1994), 33, 89-109. pdf file
  • 1995: J. Losson, J.G. Milton, & M.C. Mackey. "Phase transitions in networks of chaotic elements with short and long range interactions", Physica D (1995) 81, 177-203. pdf file
  • 1995: M.C. Mackey, & J.G. Milton. "Asymptotic stability of densities in coupled map lattices", Physica D (1995), 80, 1-17. pdf file
  • 1995: A. Rey & M.C. Mackey. "Transitions and kinematics of reaction-convection fronts in a cell population model", Physica D. (1995), 80, 120-139. pdf file
  • 1995: M.O. Vlad & M.C. Mackey. "Generating functional approach to multichannel parallel relaxation with application to the problem of direct energy transfer in fractal systems with dynamic disorder", J. Math. Phys. (1995), 36, 1834-1853. vlad-mackey-1995-generating.pdf
  • 1995: M.O. Vlad & M.C. Mackey. "Stochastic renormalization group approach to space dependent supercritical branched chain processes", Phys. Rev. A. (1995), 51, 3104-3119. pdf file
  • 1995: M.O. Vlad & M.C. Mackey. "Jump clustering, Shlesinger-Huges stochastic renormalization, and interacting Levy flights", Phys. Rev. A. (1995), 51, 3120-3125. pdf file
  • 1995: M.O. Vlad & M.C. Mackey. "Maximum information entropy approach to non-Markovian random jump processes with long memory: Application to surprisal analysis in molecular dynamics", Physica A (1995), 215, 339-360. pdf file
  • 1995: J. Losson & M.C. Mackey. "Coupled map lattices as models of deterministic and stochastic differential delay equations", Phys. Rev. E. (1995), 52, 115-128. pdf file
  • 1995: M.O. Vlad & M.C. Mackey. "Passage over a random energy barrier with dynamical disorder", Phys. Lett. A. (1995), 203, 292-299. vlad-mackey-1995-passage.pdf
  • 1995: J. Bélair, M.C. Mackey, & J.M. Mahaffy. "Age-structured and two delay models for erythropoiesis", Math. Biosci. (1995), 128, 317-346. pdf file
  • 1995: P.K. Kamthan & M.C. Mackey. "Asymptotic behaviour of densities in random maps and its thermodynamic implications", Random and Computational Dynamics (1995), 3, 157-212.  pdf file
  • 1995: J. Losson & M.C. Mackey. "Evolution of probability densities in stochastic coupled map lattices", Phys. Rev. E. (1995), 52, 1403-1417. pdf file
  • 1995: M.C. Mackey & I.G. Nechayeva. "Solution moment stability in stochastic differential delay equations", Phys. Rev. E. (1995) 52, 3366-3376. pdf file
  • 1995: A. Rey & M.C. Mackey. "Propagation of population pulses and fronts in a cell replication problem: Non-locality and dependence on the initial function", Physica D. (1995), 86, 373-395. pdf file
  • 1995: M.O. Vlad, C. Lacoursiére & M.C. Mackey. "Long memory and scaling for multiplicative stochastic processes with application to the study of population oscillations", Phys. Lett. A. (1995), 208, 99-107. pdf file
  • 1996: M.C. Mackey & J.G. Milton. "Lattices with spatially extended coupling and the statistical properties of neural populations", Proc. First Inter. Conf. Nonlin. Anal. (1996), 4, 3119-3124, de Gruyter, Berlin. pdf file
  • 1996: R. Crabb, J. Losson, & M.C. Mackey. "Dependence on initial conditions in nonlocal PDE's and hereditary dynamical systems", Proc. First Inter. Conf. Nonlin. Anal. (1996), 4, 3125-3136, de Gruyter, Berlin. pdf file
  • 1996: M.O. Vlad, J. Ross, & M.C. Mackey. "Nonequilibrium fluctuation-dissipation relations for independent random rate processes with dynamical disorder", J. Math. Phys. (1996), 37, 803-835. vlad-ross-mackey-1996-fluctuation.pdf
  • 1996: M.O. Vlad, M.C. Mackey, & B. Schönfisch. "Statistical fractals with cutoffs, Shlesinger--Hughes renormalization, and the onset of an epidemic", Phys. Rev. E. (1996), 53, 1382-1398. pdf file
  • 1996: M.O. Vlad & M.C. Mackey. "Crossover from geometrical to stochastic fractal statistics for translationally invariant random distributions of independent particles in N-dimensional Euclidean space", Chaos, Solitons, & Fractals (1996), 7, 337-348. pdf file
  • 1996: M.O. Vlad, R. Metzler, T.F. Nonnenmacher, & M.C. Mackey. "Universality classes for asymptotic behavior of relaxation processes in systems with dynamical disorder: Dynamical generalizations of stretched exponential", J. Math. Phys. (1996), 37, 2279-2306. vlad-et-al-1996-universality.pdf
  • 1996: M.O. Vlad, B. Schönfisch, & M.C. Mackey. "Fluctuation dissipation relations and universal behavior for relaxation processes in systems with static disorder and in the theory of mortality", Phys. Rev. E. (1996), 53, 4703-4710. pdf file
  • 1996: M.O. Vlad, B. Schönfisch, & M.C. Mackey. "Fractal time, long-range correlations and stretched or compressed exponential survival statistics", Fractals (1996), 4, 59-72.
  • 1996: J. Losson & M.C. Mackey. "Thermodynamic properties of coupled map lattices", in Stochastic and Spatial Structures of Dynamical Systems (eds. S.J. van Strien & S.M. Verduyn Lunel), North Holland, Amsterdam, 1996, pp 41-69.  pdf file
  • 1996: R. Crabb, M.C. Mackey, & A. Rey. "Propagating fronts, chaos and multistability in a cell replication model", Chaos (1996) 6, 477-492. pdf file
  • 1996: M.O Vlad, B. Schönfisch, & M.C. Mackey. "Fluctuating Poissonian clocks, fractal random processes and dynamical Porter-Thomas distributions--Applications to evolutionary molecular biology, enhanced diffusion and dynamical relaxation", Physica Scripta (1996), 54, 581-593. pdf file
  • 1996: M.O Vlad, B. Schönfisch, & M.C. Mackey. "Industrial replacement, communication networks and fractal time statistics", Phys. A (1996), 229, 295-311. pdf file
  • 1996: M.O Vlad, B. Schönfisch, & M.C. Mackey. "Evolution towards ergodic behavior of stationary fractal random processes with memory--Application to the study of long-range correlations of nucleotide sequences in DNA", Phys. A (1996), 229, 312-342. pdf file
  • 1996: M.O Vlad, B. Schönfisch, & M.C. Mackey. "Self-similar potentials in random media, fractal evolutionary landscapes and Kimura's theory of molecular evolution", Phys. A (1996), 229, 343-364. pdf file
  • 1997: M.O. Vlad, J. Ross, & M.C. Mackey. "Jump statistics, sojourn times, fluctuation dynamics and ergodic behaviour for Markov processes in continuous time with a finite number of states", Physica A. (1997), 243, 319-339. pdf file
  • 1997: M.O. Vlad, J. Ross, & M.C. Mackey. "Fluctuation dynamics, thermodynamic analogies and ergodic behaviour for nonequilibrium independent rate processes with dynamical disorder", Physica A. (1997), 243, 340-361.  pdf file
  • 1997: M.C. Mackey. "Mathematical models of hematopoietic cell replication and control", pp. 149-178 in The Art of Mathematical Modelling: Case Studies in Ecology, Physiology and Biofluids (H.G. Othmer, F.R. Adler, M.A. Lewis, and J.C. Dallon eds.) Prentice Hall (1997). pdf file
  • 1998: J.M. Mahaffy, J. Bélair, & M.C. Mackey. "Hematopoietic model with moving boundary condition and state dependent delay", J. Theor. Biol. (1998), 190, 135-146. pdf file
  • 1998: T. Hearn, C. Haurie, & M.C. Mackey. "Cyclical neutropenia and the peripheral control of white blood cell production", J. Theor. Biol. (1998), 192, 167-181. PDF icon hearn-haurie-mackey-1998.pdf
  • 1998: C. Haurie, D.C. Dale, & M.C. Mackey. "Cyclical neutropenia and other periodic hematological disorders: A review of mechanisms and mathematical models", Blood (1998), 92, 2629-2640.PDF icon haurie-dale-mcm-1998.pdf
  • 1999: A. Lasota & M.C. Mackey. "Statistical stability of strongly perturbed dynamical systems", Fields Institute Communications (1999), 21, 363-376.PDF icon pdf file
  • 1999: M.C. Mackey & R. Rudnicki. "A new criterion for the global stability of simultaneous cell replication and maturation processes", J. Math. Biol. (1999), 38,195-219. pdf file
  • 1999: A. Lasota & M.C. Mackey. "Cell division and the stability of cellular replication", J. Math. Biol. (1999), 38, 241-261. pdf file
  • 1999: C. Haurie, D.C. Dale, & M.C. Mackey. "Occurrence of periodic oscillations in the differential blood counts of congenital, idiopathic and cyclical neutropenic patients before and during treatment with G-CSF", Exper. Hematol. (1999), 27, 401-409. pdf file
  • 1999: C. Haurie, R. Person, D.C. Dale, & M.C. Mackey. "Hematopoietic dynamics in grey collies", Exper. Hematol. (1999), 27, 1139-1148. pdf file
  • 1999: P. Fortin & M.C. Mackey. "Periodic chronic myelogenous leukemia: Spectral analysis of blood cell counts and etiological implications", Br. J. Haematol. (1999), 104, 336-345.pdf file

 

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