- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Mathematical Physics
Volume 2014 (2014), Article ID 597012, 6 pages
Effects of a Fluctuating Carrying Capacity on the Generalized Malthus-Verhulst Model
1Departamento de Física, Facultad de Ciencias, Universidad de Tarapacá, 1000000 Arica, Chile
2Escuela Universitaria de Ingeniería Eléctrica-Electrónica, Universidad de Tarapacá, 1000000 Arica, Chile
3Instituto de Alta Investigación IAI, Universidad de Tarapacá, 1000000 Arica, Chile
Received 8 January 2014; Revised 23 April 2014; Accepted 5 May 2014; Published 4 June 2014
Academic Editor: Klaus Kirsten
Copyright © 2014 Héctor Calisto et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. L. Stratonovich, Topics in the Theory of Random Noise, Vol. I and Vol. II, Gordon and Breach Science, New York, NY, USA, 1963.
- H. Haken, Synergetic: An Introduction, Springer, Berlin, Germany, 2nd edition, 1978.
- C. W. Gardiner, Handbook of Stochastic Methods, Springer, Berlin, Germany, 1983.
- H. Risken, The Fokker-Planck Equation: Methods of Solutions and Applications, Springer, Berlin, Germany, 1984.
- W. Horsthemke and R. Lefever, Noise-Induced Transitions, Springer, Berlin, Germany, 1984.
- N. G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, The Netherlands, 1992.
- S. Ciuchi, F. De Pasquale, and B. Spagnolo, “Self-regulation mechanism of an ecosystem in a non-Gaussian fluctuation regime,” Physical Review E, vol. 54, no. 1, pp. 706–716, 1996.
- B. Spagnolo and A. La Barbera, “Role of the noise on the transient dynamics of an ecosystem of interacting species,” Physica A, vol. 315, no. 1-2, pp. 114–124, 2002.
- N. S. Goel and N. Richter-Dyn, Stochastic Models in Biology, The Blackburn Press, Caldwell, NJ, USA, 2003.
- W. E. Lamb Jr., “Theory of an optical maser,” Physical Review, vol. 134, no. 6A, pp. A1429–A1450, 1964.
- B. Pariser and T. C. Marshall, “Time development of a laser signal,” Applied Physics Letters, vol. 6, no. 12, pp. 232–234, 1965.
- R. Zygadło, “Relaxation and stationary properties of a nonlinear system driven by white shot noise: an exactly solvable model,” Physical Review E, vol. 47, no. 6, pp. 4067–4075, 1993.
- B. J. West and P. Grigolini, Complex Webs: Anticipating the Improbable, Cambridge University Press, Cambridge, UK, 2011.
- R. Herman and E. W. Montroll, “A manner of characterizing the development of countries,” Proceedings of the National Academy of Sciences of the United States of America, vol. 69, pp. 3019–3023, 1972.
- E. W. Montroll, “Social dynamics and the quantifying of social forces,” Proceedings of the National Academy of Sciences of the United States of America, vol. 75, no. 10, pp. 4633–4637, 1978.
- V. Bouché, “A new instability phenomenon in the Malthus-Verhulst model,” Journal of Physics A. Mathematical and General, vol. 15, no. 6, pp. 1841–1848, 1982.
- A. K. Das, “A stochastic approach to the freezing of supercooled liquids,” Canadian Journal of Physics, vol. 61, pp. 1046–1049, 1983.
- C. S. Pande, “On a stochastic theory of grain growth,” Acta Metallurgica, vol. 35, no. 11, pp. 2671–2678, 1987.
- C. H. Wörner, A. Olguín, M. Ortiz, O. Herrera, J. C. Flores, and H. Calisto, “Final cell distribution in a Zener pinned structure,” Acta Materialia, vol. 51, no. 20, pp. 6263–6267, 2003.
- N. S. Goel, S. C. Maitra, and E. W. Montroll, “On the Volterra and other nonlinear models of interacting populations,” Reviews of Modern Physics, vol. 43, pp. 231–276, 1971.
- H. Calisto and M. Bologna, “Exact probability distribution for the Bernoulli-Malthus-Verhulst model driven by a multiplicative colored noise,” Physical Review E, vol. 75, no. 5, Article ID 050103, 2007.
- G. E. Uhlenbeck and L. S. Ornstein, “On the theory of the Brownian motion,” Physical Review, vol. 36, no. 5, pp. 823–841, 1930.
- A. A. Dubkov and B. Spagnolo, “Verhulst model with Lévy white noise excitation,” The European Physical Journal B, vol. 65, no. 3, pp. 361–367, 2008.
- G. Aquino, M. Bologna, and H. Calisto, “An exact analytical solution for generalized growth models driven by a Markovian dichotomic noise,” Europhysics Letters, vol. 89, no. 5, Article ID 50012, 2010.
- M. Bologna and H. Calisto, “Effects on generalized growth models driven by a non-Poissonian dichotomic noise,” European Physical Journal B, vol. 83, no. 3, pp. 409–414, 2011.
- J. H. Matis and T. R. Kiffe, Stochastic Population Models, Springer, New York, NY, USA, 2000.
- P. Hanggi and P. Jung, “Colored noise in dynamical systems,” Advances in Chemical Physics, vol. 89, pp. 239–326, 1995.
- I. Bena, “Dichotomous Markov noise: exact results for out-of-equilibrium systems,” International Journal of Modern Physics B, vol. 20, no. 20, pp. 2825–2888, 2006.
- P. Allegrini, M. Bologna, L. Fronzoni, P. Grigolini, and L. Silvestri, “Experimental quenching of harmonic stimuli: universality of linear response theory,” Physical Review Letters, vol. 103, no. 3, Article ID 030602, 2009.
- I. Broussell, I. L'Heureux, and E. Fortin, “Experimental evidence for dichotomous noise-induced states in a bistable interference filter,” Physics Letters A, vol. 225, no. 1–3, pp. 85–91, 1997.
- M. Wu and C. D. Andereck, “Effects of external noise on the Fredericksz transition in a nematic liquid crystal,” Physical Review Letters, vol. 65, no. 5, pp. 591–594, 1990.
- N. G. van Kampen, “Stochastic differential equations,” Physics Reports, vol. 24, no. 3, pp. 171–228, 1976.
- C. Van den Broeck, “On the relation between white shot noise, Gaussian white noise, and the dichotomic Markov process,” Journal of Statistical Physics, vol. 31, no. 3, pp. 467–483, 1983.
- A. Fuliński, “Non-Markovian noise,” Physical Review E, vol. 50, no. 4, pp. 2668–2681, 1994.
- V. E. Shapiro and V. M. Loginov, “‘Formulae of differentiation’ and their use for solving stochastic equations,” Physica A, vol. 91, no. 3-4, pp. 563–574, 1978.
- M. Bologna, K. J. Chandía, and B. Tellini, “Stochastic resonance in a non-Poissonian dichotomous process: a new analytical approach,” Journal of Statistical Mechanics: Theory and Experiment, no. 7, Article ID P07006, 2013.
- P. Allegrini, P. Grigolini, and B. J. West, “Dynamical approach to Lévy processes,” Physical Review E, vol. 54, no. 5, pp. 4760–4767, 1996.
- M. Bologna and P. Grigolini, “Lévy diffusion: the density versus the trajectory approach,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2009, no. 3, Article ID P03005, 2009.
- M. Bologna, “Asymptotic solution for first and second order linear Volterra integro-differential equations with convolution kernels,” Journal of Physics A. Mathematical and Theoretical, vol. 43, no. 37, Article ID 375203, 2010.
- S. Ciuchi, F. De Pasquale, and B. Spagnolo, “Nonlinear relaxation in the presence of an absorbing barrier,” Physical Review E, vol. 47, no. 6, pp. 3915–3926, 1993.