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Minorsky’s equation; nonlinear derivative feedback; time delay; complex dynamics; P-spice and microcontroller simulations; electronic circuit realisation

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.

NGOUABO ULRICH GAËL^{1 2} NOUBISSIE SAMUEL^{2 3} FOTSIN HILAIRE BERTRAND¹ WOAFO PAUL³

1. Unité de Recherche de Matière de Condensée d’Electronique et de Traitements de Signal (UR-AMCETS), Faculté des Science, Université de Dschang, B.P. 67, Dschang, Cameroun
2. Unité de Recherche d’Ingénierie des Systèmes Industriels et Environnement (UR-ISIE), IUT-FV de Bandjoun, Université de Dschang, P.B. 134, Bandjoun, Cameroun
3. Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes and TWAS Research Unit, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaounde, Cameroun

Published

1 January 2020

Manuscript received

18 March 2019

Manuscript revised

13 July 2019

Accepted

22 August 2019

Early published

Unedited version published online

Final version published online

18 December 2019