Bifurcations and chaotic behavior on the Lanford system

The aim of this article is to investigate in details the bifurcation behavior and show existence of chaotic solutions in the Lanford system. The regular behavior of the model was thoroughly studied in [Theory and Applications of Hopf Bifurcation, Cambridge University Press, 1981; Theory of Chaos, Bulgarian Acad. Press, 2001]. Using Lyapunov–Andronov theory, we define the analytical formulas for the first Lyapunov value (this is not Lyapunov exponent) at the boundaries of stability. Here, for specific parametric choice, we obtain chaotic behavior of the Lanford system for the first time to our knowledge. We also calculate the maximal Lyapunov exponent in the parameters space where chaotic motion of this system exists.