Theoretical foundation for the discrete dynamics of physicochemical systems: Chaos, self-organization, time and space in complex systems.
Gontar, V. (1997)
Discrete Dynamics in Nature and Society
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Gontar, V. (1997)
Discrete Dynamics in Nature and Society
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K. E. Gordon, I. M.M. van Leeuwen, S. Laín, M. A.J. Chaplain (2009)
Mathematical Modelling of Natural Phenomena
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In this paper we investigate the role of spatial effects in determining the dynamics of a subclass of signalling pathways characterised by their ability to demonstrate oscillatory behaviour. To this end, we formulate a simple spatial model of the p53 network that accounts for both a negative feedback and a transcriptional delay. We show that the formation of protein density patterns can depend on the shape of the cell, position of the nucleus, and the protein diffusion rates. The temporal...
Marciniak-Czochra, Anna, Kimmel, Marek (2006)
Computational & Mathematical Methods in Medicine
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Gontar, V. (2004)
Discrete Dynamics in Nature and Society
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Chay, Teresa Ree, Lee, Young Seek (1998)
Discrete Dynamics in Nature and Society
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Plank, M.J., Sleeman, B.D., Jones, P.F. (2002)
Journal of Theoretical Medicine
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Oppenheim, Ariella, Ben-Nun-Shaul, O., Mukherjee, S., Abd-El-Latif, M. (2008)
Computational & Mathematical Methods in Medicine
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Plath, P.J., Plath, J.K., Schwietering, J. (1997)
Discrete Dynamics in Nature and Society
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Herrero, Miguel A., López, José M. (2005)
Journal of Theoretical Medicine
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Carlos Graván, Rafael Lahoz-Beltra (2004)
International Journal of Applied Mathematics and Computer Science
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One of the classical problems of morphogenesis is to explain how patterns of different animals evolved resulting in a consolidated and stable pattern generation after generation. In this paper we simulated the evolution of two hypothetical morphogens, or proteins, that diffuse across a grid modeling the zebra skin pattern in an embryonic state, composed of pigmented and nonpigmented cells. The simulation experiments were carried out applying a genetic algorithm to the Young cellular...