Titlebook: Mathematical Models in Natural Science and Engineering; Juri I. Neimark Book 2003 Springer-Verlag Berlin Heidelberg 2003 Dynamical systems

harrow

Soiling a water reservoir with a bay and the Caspian Sea puzzles,Polluting a water reservoir with sewage of dissolvable pollutants. The Caspian Sea puzzles. Soiling a water reservoir through a bay. Regulating a water regime and salinity.

prosperity

Dynamics in coexistence of populations,The mathematical models for the coexistences of the types “predator — prey”, competition (opposition) and symbiosis. The phase and bifurcation portraits.

恶名声

overreach

Mathematical model for the immune response of a living organism to an infectious invasion,The simplified phenomenological model in the form of the fourth-order differential equation system for the immune response of the organism to an infection. Basic variants of the disease progress, its dependence upon parameters; the extent of the infection and the treating counteractions.

商店街

,Mathematical model for the community “Producers — Products — Managers”,Possible kinds of phase portraits. Evolution of the community with the growth of technologies and its dependence upon other parameters.

表示向前

Linear oscillators,A mathematical model for the linear oscillator. Possible kinds of motions. Phase and bifurcation portraits. The motions described by a linear oscillator: equilibrium states, harmonic, dissipative and divergent oscillations.

hypotension

construct

vasculitis

Soft and hard regimes of exciting auto-oscillations,Constructing phase and bifurcation portraits for soft and hard excitations of auto-oscillations on the basis of a point mapping study.

Progesterone

,Stochastic oscillator (the “contrary clock”),An oscillator of an unpredictable behaviour. A mathematical model, a phase portrait and a point mapping. Unpredictability and randomness. Two kinds of behaviour of dynamical systems. Stability and instability, predictability and unpredictability. An oscillator (a dynamical system) as a generator of stochastic oscillations.