Akgakaya HR, Ginzburg LR, Slice D, and Slobodkin LB (1988) The theory of population dynamics - II. Physiological delays. Bulletin of Mathematical Biology 50(5): 503-515.
Alee WC (1931) Animal Aggregations - A Study in General Sociology. Chicago: University of Chicago Press.
Augustin JC and Carlier V (2000) Mathematical modelling of the growth rate and lag time for Listeria monocytogenes. International Journal of Food Microbiology 56: 29-51.
Baranyi J (2002) Stochastic modelling of bacterial lag phase. International Journal of Food Microbiology 73: 203-206.
Baranyi J and Roberts TA (1994) A dynamic approach to predicting bacterial growth in food. International Journal of Food Microbiology 23: 277-294.
Baranyi J, Roberts TA, and McClure PJ (1993) A non-autonomous differential equation to model bacterial growth. Food Microbiology 10: 43-59.
Baty F and Delignette-Muller ML (2004) Estimating the bacterial lag time: Which model, which precision? International Journal of Food Microbiology 91: 261-277.
Buchanan RL, Whiting RC, and Damert WC (1997) When is simple good enough: A comparison of the Gompertz, Baranyi, and three-phase linear models for fitting bacterial growth curves. Food Microbiology 14: 313-326.
Carlson T (1913) Uber Geschwindigkeit and Grosse der
Hefevermerbrung in würze. Biochemische Zeitschirft 57: 313-334.
Farber JM, Cai Y, and Ross WH (1996) Predictive modeling of the growth of Listeria monocytogenes in CO2 environments. International Journal of Food Microbiology 32: 133-144.
Galilei G (1632) Dialogo Sopra i Due Massimi Sistemi Del Mondo (Dialogue Concerning the Two Chief World Systems) Florence.
Gibson AM, Bratchell N, and Roberts TA (1988) Predicting microbial growth: Growth responses of salmonellae in a laboratory medium as affected by pH, sodium chloride and storage temperature. International Journal of Food Microbiology 6: 155-178.
Ginzburg LR (1986) The theory of population dynamics: I. Back to first principles. Journal of Theoretical Biology 122: 385-399.
Gompertz B (1825) On the nature of the function expressive of the law of human mortality, and a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London 115: 513-583.
Hills BP and Wright KM (1995) Multi-compartment kinetic models for injury, resuscitation, induced lag and growth in bacterial cell populations. Food Microbiology 12: 333-346.
Hutchinson GE (1948) Circular casual systems in ecology. Annals of the New York Academy of Sciences 50: 211-246.
Maier RM (1999) Bacterial growth. In: Maier RM, Pepper IL, and Gebra CP (eds.) Environmental Microbiology, 44pp. San Diego: Academic publisher.
Malthus TR (1798) An Essay on the Principle of Population. Harmondsworth: Penguin.
May M Robert and Sir (1973) Time-delay versus stability in population models with two and three trophic levels. Ecology 54: 315-325.
May M Robert and Sir (1978) Mathematical aspects of the dynamics of animal populations. In: In: Levin SA (ed.) Studies in Mathematical Biology - Part II: Populations and Communities, Studies in Mathematics, vol. 16, pp. 317-366. Washington, DC: The Mathematical Association of America.
May M Robert and Sir (1981) Models for single populations. In: May RM (ed.) Theoretical Ecology, pp. 5-29. Oxford: Blackwell Scientific Publications.
McClure PJ, Baranyi J, Boogard E, Kelly TM, and Roberts TA (1993) A predictive model for the combined effect of pH, sodium chloride and storage temperature on the growth of Brochothrix thermosphacta. International Journal of Food Microbiology 19: 161-178.
McClure PJ, Cole MB, and Davies KW (1994) An example of the stages in the development of a predictive mathematical model for microbial growth: The effects of NaCl, pH and temperature on the growth of Aeromonas hydrophila. International Journal of Food Microbiology 23: 359-375.
McKellar R and Lu X (2003) Modeling Microbial Responses in Foods. Boca Raton: CRC Press, (ISBN 0-8493-1237-X).
McMeekin TA, Olley J, Ratkowsky DA, and Ross T (2002) Predictive microbiology: Towards the interface and beyond. International Journal of Food Microbiology 73: 395-407.
McMeekin TA and Ross T (2002) Predictive microbiology: Providing a knowledge-based framework for change management. International Journal of Food Microbiology 23: 359-375.
Messen W, Verluyten J, Leroy F, and De Vuyst L (2002) Modelling growth and bacteriocin production by Lactobacillus curvatus LTH 1174 in response to temperature and pH values used for European sausage fermentation processes. International Journal of Food Microbiology 81: 41-52.
Meyer PS (1994) Bi-logistic growth. Technological Forecasting and Social Change 47: 89-102.
Meyer PS and Ausubel JH (1999) Carrying capacity: A model with logistically varying limits, Technological Forecasting and Social Change 47: 89-102.
Monod J (1942) Recherches Sur la Croissance des Cultures Bacteriennes. Paris: Herman.
Murray BG (1992) Research methods in physics and biology. Oikos 64: 594-596.
Newton Issac, Sir (1687) Philosophiae Naturalis Principia Mathematica.
O'Donovan L and Brooker JD (2001) Effect of hydrolysable and condensed tannins on growth, morphology and metabolism of Streptococcus gallolyticus (S. caprinus) and Streptococcus bovis. Microbiology 147: 1025-1033.
Pearl R (1927) The growth of populations. The Quarterly Review of Biology II(4): 532-548.
Pirt SJ (1975) Growth lag. In: Principles of Microbe and Cell Cultivation. London: Blackwell.
Richards FJ (1959) A flexible growth function for empirical use. Journal of Experimental Botany 10: 290-300.
Smith FE (1963) Population dynamics in Daphnia magma. Ecology 44: 651-663.
Swinnen IAM, Bernaerts K, Dens EJJ, Geeraerd AH, and Van Impe JF (2004) Predictive modeling of the microbial lag phase: A review. International Journal of Food Microbiology 94: 137-159.
Tsoularis A and Wallace J (2002) Analysis of logistic growth models. Mathematical Biosciences 179: 21-55.
Turchin P (2001) Does population ecology have general laws? Oikos 94: 17-26.
Turner ME, Jr., Bradley EL, Jr., and Kirk KA (1976) A theory of growth. Mathematical Biosciences 29: 367-373.
Vadasz P and Vadasz AS (2002) The neoclassical theory of population dynamics in spatially homogeneous environments - Part I: Derivation of universal laws and monotonic growth. Physica A 309(3-4): 329-359.
Vadasz P and Vadasz AS (2002) The neoclassical theory of population dynamics in spatially homogeneous environments - Part II: Nonmonotonic dynamics, overshooting and oscillations. Physica A 309(3-4): 360-380.
Vadasz P and Vadasz AS (2006) Biological implications from an autonomous version of Baranyi & Roberts growth model. International Journal of Food Microbiology 114: 357-365.
Vadasz P and Vadasz AS (2005) Predictive modeling of microorganisms: LAG and LIP in monotonic growth. International Journal of Food Microbiology 102: 257-275.
Vadasz AS, Vadasz P, Abashar ME, and Gupthar AS (2001) Recovery of an oscillatory mode of batch yeast growth in water for a pure culture. International Journal of Food Microbiology 71(2-3): 219-234.
Vadasz AS, Vadasz P, Abashar ME, and Gupthar AS (2002) Theoretical and experimental recovery of oscillations during batch growth of a mixed culture of yeast in water. World Journal of Microbiology & Biotechnology 18(3): 239-246.
Vadasz AS, Vadasz P, Gupthar AS, and Abashar ME (2002) Theoretical and experimental recovery of oscillations during batch yeast growth in a pure culture subject to nutritional stress. Journal of Mechanics in Medicine and Biology 2(2): 147-163.
Verhulst PF (1838) Notice sur la loi que la population suit dans son accroissement. Correspondence Mathématique et Physique Publiee par A. Quetelet Tome X: 113-121.
von Bertalanffy L (1957) Quantitative laws in metabolism and growth. Quarterly Review of Biology 32: 217.
WangerskyPJ and Cunningham WJ (1957) Time lag in population models. Cold Spring Harbor Symposia on Quantitative Biology 22: 329-338.
Zwietering MH, Jongenburger I, Rombouts FM, and van't Riet K (1990) Modeling of the bacterial growth curve. Applied Environmental Microbiology 56: 1875-1881.
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