The phenomenological model of the urban agglomeration dynamics: theoretical aspect

The article provides the phenomenological analysis of the influence of centrifugal and centripetal forces on the agglomerative process. The paper shows the possibility of applying mathematical models for assessing the resulting effect of their impact on the urban agglomeration. The phenomenological description is carried out by means of the phase space, the dynamic space, the space of parameters and a certain mathematical model. The urban agglomeration population as an indicator of the economic activity concentration and the change of population number are taken as the main phase variables. At certain restrictions to the type of functional dependence of change rates of population concentration on its number the following phenomena can be observed: self-oscillations; damped oscillations; fluctuations with an increasing, but limited in the asymptotics amplitude; monotonous achievement of the stable balance from above or from below (logistic dependence); steady, semi-steady or unstable limit cycles of various lengths. The characteristic feature of self-oscillations is the lack of external periodic effect. The general qualitative behavior of the system in the whole dynamic space is manifested at t when its asymptotic characteristics donot depend on entryconditions. Themost important solutions are stationary points and limit cycles. The problem ofstabilityand the nature of stationary points are directly connected with the qualitative image of the phase plane portrait in their environment and its topology. The type of phase plane portraits depends on the model parameters and is defined bythe type of the special point. The article provides the theoretical phase plane portraits of the urban agglomeration dynamics for different types of static correlation between growth rates of the agglomeration population and economic activity concentration. The paper presents the current phase plane portrait of the Vladivostok urban agglomeration.