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Dynamical System: An Overview

Srikanth Nuthanapati

The idea of a dynamical system emerges from Newtonian mechanics. There, as in other natural sciences and engineering disciplines, the evolution rule of dynamical systems is an implicit relation that gives the system’s state only for a short time in the future. Finding an orbit required sophisticated mathematical techniques and could only be accomplished for a small class of dynamical systems prior to the advent of computers. The task of determining the orbits of a dynamical system has been simplified thanks to numerical methods implemented on electronic computing machines. A dynamical system is a mathematical system in which a function describes the time dependence of a point in a geometrical space. Mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish in a lake each spring are some examples. A dynamical system is defined in physics as a “particle or ensemble of particles whose state changes over time and thus obeys differential equations involving time derivatives.” An analytical solution of such equations or their integration over time via computer simulation is realized to make a prediction about the system’s future behaviour