Antoni Leon Dawidowicz

Age-dependent Population Dynamics with the Delayed Argument

The model of age-dependent population dynamics was for the first time described by von Foerster (1959) This model is based on the first-order partial differential equation with the standard initial condition and the nonlocal boundary condition in integral form. Gurtin and MacCamy in their paper (1974) analyzed the more general model, where the progress of the population depends on its number. They established the existence of the unique solution of this model for all time. In our presentation the results of Gurtin and MacCamy will be generalized on the case, when the dependence on number of population is delayed.

A Mathematical Model of the Bioenergetic Processes in Green Plants

The bioenergetic phenomena occurring in green plants are described by three equations for biomass, ATP level, and the level of inorganic phosphorus. The well-posedness of the problem is proved. Simulations show that the bioenergetic processes are oscillatory with sunlight.

Asymptotic properties of the Lasota equation in various functional spaces

We present asymptotic properties of the linear Lasota equation in various functional spaces: Holder, Lp and Orlicz spaces. We give also the conditions of stability and chaos in the sens of Devaney in a Holder space for the dynamical system generated by the non-linear Lasota equation.

The speech - a specific feature of the evolution of the modern human (Homo sapiens)

The specific feature of humans, that distinguishes them from the animal world, is the speech. The speech is a form of communication in which we use comprehensive signs to express verbally ourselves and the surrounding reality. This definition imposes the opinion that the origin of the speech can be considered from the appropriately high level of the brain development. In order to trace the evolution of the ability to speak among the Primates, the measurements of the superofacial triangle of the splanchnocranium, according to Martin and Saller (1957), were carried out. The triangle characterises the distribution of the organs responsible for articulation of the sounds. The mathematical analysis concerned i.a. the descriptive statistics of the measurements, illustrated with the bar charts. On this basis, the Mahalanolobis distances between the examined taxons of primates were measured and presented graphically in form of the discriminant analysis. The applied model helped to divide entirely the monkey and apes from the Hominidae, and to form two clusters of taxons.xa0 The conclusion is that the ability to speak is a sign of a quality change in the evolution of the Primates that led to the Homo sapiens form. Animals do not use such a wide spectrum of recognizing the surrounding reality and their interactive communication is based on the experience and instinct.

On the Multispecies Delayed Gurtin-MacCamy Model

The paper deals with the description of multispecies model with delayed dependence on the size of population. It is based on the Gurtin and MacCamy model. The existence and uniqueness of the solution for the new problem of populations dynamics are proved, as well as the asymptotical stability of the equilibrium age distribution.