Dynamical Systems. Part 1: Definition of dynamical system (by Natalia Janson) скачать в хорошем качестве

Dynamical Systems. Part 1: Definition of dynamical system (by Natalia Janson)

Mathematical modelling of physiological systems: Dynamical Systems. Part 1: Definition of dynamical system. This lecture introduces the concept of a system evolving with time *spontaneously*, i.e. on its own and not thanks to any external rhythmic disturbance, such as a swinging pendulum or a beating heart. Such systems can be mathematically described as dynamical systems, i.e. as combinations of first-order ordinary differential equations, which are generally non-linear. Equations like this are usually impossible to solve analytically. To aid understanding and prediction of their behaviour, a special mathematical object called velocity vector field can be introduced. More explanation of a velocity vector field and its interpretation can be found in a Supplementary Note to [Janson & Marsden "Dynamical system with plastic self-organized velocity field as an alternative conceptual model of a cognitive system", Scientific Reports (Nature publishing group) vol. 7, 17007 (2017)] and [Janson "Nonlinear dynamics of biological systems", Contemporary Physics 53:2, 137-168 (2012)]. #modelling #dynamical #system #living #system #biological #physiological #modeling #mathematical #modelling #attractor #oscillation #synchronization #synchronisation #phase #realization #realisation #limit #cycle #clock #heart #pacemaker Natalia Janson's home page https://sites.google.com/view/natalia...