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.

In 1970, Keller and Segel have offered parabolic systems to illustrate the aggregation process of cellular slime mold by the chemical attraction [

The local solutions were studied by the second author [

As V.M. Alexandrov wrote in the introduction of a well-liked science book

The purpose of this paper is to derive analytical solutions of attractor one-dimensional Keller-Segel equations (

The paper is prearranged as follows: in Section

With the purpose of making the fundamental possessions of the homotopy decomposition method [

Where

In this section we apply this method for solving coupled attractor one-dimensional Keller-Segel equations.

Consider the following Keller Segel equation with the sensitivity function

Then the chemotactic term

Figures

Biological behaviour of concentrations of the chemical substance and amoebae as function of space.

Biological behaviour of concentrations as function of time.

The behaviour of the coupled solutions.

Consider the following Keller-Segel equation with the sensitivity function

With the chemotactic term

Second case, we suppose that

The above figures show the behaviour of the solution of the system of (

Coupled solutions.

Coupled solutions.

Coupled solutions.

Coupled solutions.

Consider the following Keller-Segel equation with the sensitivity function

With the chemotactic term

The homotopy decomposition method is chosen to solve this kind of nonlinear problem. Because of the following advantages that, the HDM has over the exiting methods. The method does not require the linearization or assumptions of weak nonlinearity [

An interesting biological problem describing theaggregation process of cellular slime mold by the chemical attraction was investigated in this paper. We made use of the efficient method called homotopy decomposition method to derive the solution of the mathematical equation underpinning this problem. Analysis and results of nonlinear system of attractor one-dimensional Keller-Segel equation indicate that the model matches the regular biological diffusion behaviour observed in the field.

The authors declare that they have no conflict of interests.

Abdon Atangana wrote the first draft, P. D. Vermeulen revised the paper, and all the authors corrected the last version.