| Partner: Richard Gejji |
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Recent publications
| 1. | Gejji R.♦, Kaźmierczak B., Alber M.♦, Classification and stability of global inhomogeneous solutions of a macroscopic model of cell motion, MATHEMATICAL BIOSCIENCES, ISSN: 0025-5564, DOI: 10.1016/j.mbs.2012.03.009, Vol.238, pp.21-31, 2012 Abstract: Many micro-organisms use chemotaxis for aggregation, resulting in stable patterns. In this paper, the amoeba Dictyostelium discoideum serves as a model organism for understanding the conditions for aggregation and classification of resulting patterns. To accomplish this, a 1D nonlinear diffusion equation with chemotaxis that models amoeba behavior is analyzed. A classification of the steady state solutions is presented, and a Lyapunov functional is used to determine conditions for stability of inhomogenous solutions. Changing the chemical sensitivity, production rate of the chemical attractant, or domain length can cause the system to transition from having an asymptotic steady state, to having asymptotically stable single-step solution and multi-stepped stable plateau solutions. Keywords:Aggregation, Chemotaxis, Inhomogenous stability, Lyapunov functional, Plateau solutions, Dictyostelium discoideum Affiliations:
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| 2. | Alber M.♦, Gejji R.♦, Kaźmierczak B., Existence of global solutions of a macroscopic model of cellular motion in a chemotactic field, APPLIED MATHEMATICS LETTERS, ISSN: 0893-9659, DOI: 10.1016/j.aml.2009.05.013, Vol.22, No.11, pp.1645-1648, 2009 Abstract: Existence of global classical solutions of a class of reaction–diffusion systems with chemotactic terms is demonstrated. This class contains a system of equations derived recently as a continuous limit of the stochastic discrete cellular Potts model. This provides mathematical justification for using numerical solutions of this system for modeling cellular motion in a chemotactic field. Keywords:Reaction–diffusion systems, Nonlinear diffusion, Global existence, Continuous limit, Cellular motion, Chemotaxis Affiliations:
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