Analytical studies on third-order chaotic systems with Sprott type nonlinearities and their microcontroller implementation

Abstract

The evolution of chaos in a generic third-order autonomous mathematical model with nonlinearities described by simple mathematical functions is reported in this paper. The nonlinearities termed as Sprott type nonlinear functions are used in the design of a class of third-order systems exhibiting chaotic behavior. The evolution and confirmation of chaos in their system dynamics is observed through numerical simulation studies of one-parameter bifurcation diagrams and Lyapunov exponents. Analytical solutions are developed for systems with piecewise-linear nonlinear functions. Finally, the microcontroller implementation of the third-order system equations with different nonlinearities and analog circuit simulation results are presented to confirm the numerical and analytical results. Chaos in generic third-order systems studied through numerical, analytical and microcontroller results has been reported in the literature for the first time.