Numerical and microcontroller simulations, and electronic circuit realisation of Minorsky’s equation

This work deals with the mathematical analysis, numerical and microcontroller simulations and electronic circuit realisation of the dynamics of Minorsky’s equation. We consider the model including the nonlinear derivative feedback with delay. The study of stability is done by linearising the equation. An alternation between the zones of stability and instability as a function of the values of the delay is found. The bifurcation diagrams allowed us to validate the analytical predictions. These bifurcation diagrams show Hopf bifurcations and complex dynamics of the system. The analog and microcontroller simulations together with the experimental analysis were carried out in order to validate the theoretical analysis.