Two common examples of one-dimensional maps (the tent map and the logistic map) are generalized to cases where they have more than one control parameter. In the case of the tent map, this still allows the global Lyapunov exponent to be found analytically, and permits various properties of the resulting global Lyapunov exponents to be investigated…

A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help…

A simple model for how traffic moves around a closed loop of road is introduced. The consequent analysis of the model can be used as an application of techniques taught at first year undergraduate level, and as a motivator to encourage students to think critically about model formulation and interpretation.

Introduces some of the basic techniques of cryptography along with examples of how cryptography can be employed in teaching mathematics and used as a cross curricular theme. (Author/ASK)

Two simple mathematical models for how individual vehicles follow each other along a stretch of road are discussed. The resulting difference equations can be used as applications of techniques taught at A-level and first year undergraduate level, and as an introduction to the behaviour of the logistic map.