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

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Introduction,gical, cybernetical and other systems and processes. In addition, this book will help you to form your own scientific understanding and attitude towards “applied mathematics”, and other mathematical subjects you are studying.
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Dynamical systems,ical system as a basic mathematical model in the natural sciences. A phase portrait. Examples of dynamical systems and their phase portraits. A phase portrait as a means of geometrical representation of our knowledge about a dynamical system and as a means of its study.
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Fluid outflow from a vessel,The Torrichelli law and a simplest model of the fluid outflow. Compression of the outflowing water jet. Insufficiency of a simplest model and improvements with the account of the fluid outflow speedup. The phase portrait for a fast speedup and a slow outflow.
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Equilibrium and auto-oscillations of fluid level in the vessel with simultaneous inflow and outflowDynamics of fluid level when the outflow through a bottom hole or a siphon and when a constant inflow are present.
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Transitive processes, equilibrium states and auto-oscillations,ossible types of motions — transient processes, stable equilibrium states and auto-oscillations.
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Dynamics of the water surface level in a reservoired hydropower station,A phase portrait and equilibrium regimes for a hydropower station. Critical values. Bifurcation diagram.
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Energetic model of the heart,Types of crisis states and crucial values. Narrowing the vital capabilities.
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