Investigation Of Systematic Dynamics And Computer Simulation For Biological Wave Characteristics Of Popular Growth-Multiplication Of Single-Species Bacillus Systems

It is well known that biological and ecological system is the very complex dynamical system. The biology is very complex and ordered in the function and the structure. Based on the dissipative structure theories created by Prigogine and the synergenics theories proposed by Haken, Self-organization theory in no-equilibrium systems is suggested. This theory is successfully applied to investigate the classic chemical and physical systems, meanwhile to study the biological and the ecological systems using the self-organization theory has been issues of great theoretical and practical importance. A series of results describing biological wave characteristics of popular growth of single-species bacillus systems governed by birth and death-diffusion dynamical equation are summarized as follows. In the first chapter of this thesis, Logistic equations describing the relations of the popular quantity with the growth time and the self-organization theory describing the spatial-temporal dynamics of the popular growth for the given population are Summarized. In the next chapters, the modified Logistic equations and the partial differential equations theories are successfully used to study the spatial-temporal dynamics of the popular growth for the single-species bacillus systems.In the second chapter of this thesis, based on the theories of the cellar biology a b|irth and death-diffusion dynamical equation valid for the popular growth ofsingle-species and single-sources bacillus system is established by means of the non-linear method of the systematic dynamics. Furthermore, the traveling wave solution and its stability of this dynamical evolutionary equation are studied by means of mathematical analysis. Under the special initial values and boundary conditions corresponding to the point-source growth, the simplified dynamical evolutionary equations are considered by means of the computer simulation. A series of results of computer simulations for the simplified dynamical evolutionary equations are helpful to explore more complex system describing the popular growth of single-species and single-sources bacillus and the evolution of the nutrition in the next chapter.In the chapter 3 and 4, a series of biological wave characteristics such as the opening features, the single-directional features, the adaptation, the stability, the chemotaxis, the synchronism and the rhythm are observed by means of experiments for the Proteus mirabilis. Based on the theories of cellar biology, the experimental phenomena of chemical waves, parabolic equation theories and experimental observations of the biological wave characteristics a dynamical model of birth and death-diffusion type has been suggested for the popular growth of single-species bacillus system. It has been verified that the two-variable evolutionary equation of this model has the traveling wave solutions. Furthermore, under the special initial values and boundary conditions corresponding to the point-source growth, these dynamical evolutionary equations are analyzed by means of the computer simulation. It shows that the popular growth of single-species bacillus systems governed by birth and death-diffusion dynamical equation is characterized by a spatial-temporal quasi-periodic property in which is consistent with both the traveling wave solution and the biological wave behavior respectively obtained by theoretical research and experimental observation. A series of results of computer simulations describing the popular growth of single-species and single-sources bacillus are given. It turns out that these computer simulation results we obtain are qualitatively in agreement with some results from experimental observations. The energy-saving features of the biological wave for the Proteus mirabilis are qualitatively copied by means of thecomputer simulation. These exploratory results are helpful to complete the biological wave theory.In the last chapter of this thesis, based on both the theories of cellar biology and the results of experimental observations for the biological wave c...