We will also discuss flywheels, which were used in steam engines to keep the motion reasonably uniform and so prevent explosions. Simple biological and chemical systems provide a good introduction to dynamical systems, which is the mathematical study of the behavior of nonlinear systems. There are countless biological systems that have been observed in nature. Here the essential question is how well we can model simple, but practical, chemical reactions. Finally, we will discuss the basics of the Hodgkin-Huxley model of nerve conduction, which describes how nerve impulses are transmitted through our bodies.
Many dynamical systems can be chaotic in certain parameter regimes.
We will study very simple chaotic systems, since these are complicated enough. The lessons learned should help us understand why many of the systems we have discussed above can be chaotic. To see that there is a fundamental difference between chaos and randomness, we will explore how to use chaos to send secret messages. Traffic flow provides a simple introduction to systems of ordinary differential equations and differentialdelay equations. For individual particles we use a statistical approach to systems of ordinary differential equations.