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Modelling the aggregation process of cellular slime mold by the chemical attraction.

Atangana A, Vermeulen PD - Biomed Res Int (2014)

Bottom Line: We put into exercise a comparatively innovative analytical modus operandi, the homotopy decomposition method (HDM), for solving a system of nonlinear partial differential equations arising in an attractor one-dimensional Keller-Segel dynamics system.Numerical solutions are given and some properties show evidence of biologically practical reliance on the parameter values.The reliability of HDM and the reduction in computations give HDM a wider applicability.

View Article: PubMed Central - PubMed

Affiliation: Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa.

ABSTRACT
We put into exercise a comparatively innovative analytical modus operandi, the homotopy decomposition method (HDM), for solving a system of nonlinear partial differential equations arising in an attractor one-dimensional Keller-Segel dynamics system. Numerical solutions are given and some properties show evidence of biologically practical reliance on the parameter values. The reliability of HDM and the reduction in computations give HDM a wider applicability.

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Coupled solutions.
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fig5: Coupled solutions.

Mentions: The above figures show the behaviour of the solution of the system of (20) with initial conditions in (21) and (26). These solutions are describing the concentrations of the chemical substance and the amoebae in the human body for a given set of theoretical parameters chosen according to the literatures. While on one hand, Figure 4 shows the behaviour as function of space, Figures 5, 6, and 7 show the behaviour of these solutions as function of time. From the above figures, one can deduce that the concentration of amoebae reduces in space as the concentration of the chemical substance reduces. It is observed from the graphical representation that the approximate solutions obtained display the behaviour of the real world problem.


Modelling the aggregation process of cellular slime mold by the chemical attraction.

Atangana A, Vermeulen PD - Biomed Res Int (2014)

Coupled solutions.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4121043&req=5

fig5: Coupled solutions.
Mentions: The above figures show the behaviour of the solution of the system of (20) with initial conditions in (21) and (26). These solutions are describing the concentrations of the chemical substance and the amoebae in the human body for a given set of theoretical parameters chosen according to the literatures. While on one hand, Figure 4 shows the behaviour as function of space, Figures 5, 6, and 7 show the behaviour of these solutions as function of time. From the above figures, one can deduce that the concentration of amoebae reduces in space as the concentration of the chemical substance reduces. It is observed from the graphical representation that the approximate solutions obtained display the behaviour of the real world problem.

Bottom Line: We put into exercise a comparatively innovative analytical modus operandi, the homotopy decomposition method (HDM), for solving a system of nonlinear partial differential equations arising in an attractor one-dimensional Keller-Segel dynamics system.Numerical solutions are given and some properties show evidence of biologically practical reliance on the parameter values.The reliability of HDM and the reduction in computations give HDM a wider applicability.

View Article: PubMed Central - PubMed

Affiliation: Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa.

ABSTRACT
We put into exercise a comparatively innovative analytical modus operandi, the homotopy decomposition method (HDM), for solving a system of nonlinear partial differential equations arising in an attractor one-dimensional Keller-Segel dynamics system. Numerical solutions are given and some properties show evidence of biologically practical reliance on the parameter values. The reliability of HDM and the reduction in computations give HDM a wider applicability.

Show MeSH