Simulation of biological waves in single-species bacillus system governed by birth and death-diffusion dynamical equation

Based on both the theories of cellar biology and the results of experimental observations a dynamical model of birth and death-diffusion type has been suggested for popular growth of bacillus and evolution of nutrition in the single-species bacillus system with a growth–propagation source. It has been verified that the single-species bacillus system in the process of growth–propagation has the biological wave behaviors from the experimental observation. Furthermore, under a special initial values and boundary conditions corresponding to the point-source growth in a closed culture-container, the evolutionary equations of this dynamical model in the single-species bacillus system with a growth–propagation source and the combination of biological waves in the single-species bacillus system with two growth–propagation sources are analyzed by means of the computer simulation, respectively. It shows that the popular growth of single-species bacillus systems governed by birth and death-diffusion dynamical equation is characterized by the spatial-temporal quasi-periodicities which is consistent with the traveling wave solution of above evolutionary equations. It turns out that these results of computer simulation, we obtain could qualitatively copy and describe the phenomenon from experimental observations. The results reported in this paper are a powerful support to the famous argument of the biological wave about the popular growth of bacteria based on lab-observation in ecology.