The work is devoted to the systematic research of the periodic, quasi-periodic or chaotic oscillations and the coexistence in the nonlinear Duffing-van der Pol type dynamical systems describing processes and phenomena in nature or engineering. The achieved result is the elaboration of the basic theory for searching nonlinear effects based on the concepts of periodic skeletons, bifurcation theor...

In this paper, a method for identifying the chaotic state of duffing oscillator is proposed where the duffing oscillator is used for weak signal detection. This method is based on frequency spectrum analysis and filtering. Some relative aspects of this method for practical using are studied in details too. The proposed method has three properties; reasonable calculation complexity, robustness t...

Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s w...

The Lyapunov based approach for synchronizing and identifying the unknown parameters in the Duffing system is presented in this paper. The strategy consists of proposing a slave system which has to follow asymptotically the desired Duffing system. The gains of the slave system are adjusted continually according to a convenient adaptation control law, until the measurable output error converges ...

Periodic solutions of a harmonically forced Duffing oscillator with time-delay state feedback are investigated using the incremental harmonic balance method. In process solving, explicit effect matrix time delay term was derived. The stability periodic determined by method which combines continuous approximation and multivariable Floquet theory. On this basis, frequency–amplitude response curve...

The dynamic characteristics of the 3:1 super-harmonic resonance response Duffing oscillator with fractional derivative are studied. Firstly, approximate solution amplitude-frequency system is obtained by using periodic characteristic response. Secondly, a set critical parameters for qualitative change derived according to singularity theory and two types responses obtained. Finally, components ...

Abstract The robustness of a chaos-suppressing scenario against potential mismatches is experimentally studied through the universal model damped, harmonically driven two-well Duffing oscillator subject to non-harmonic excitations. We consider second order analogous electrical circuit having an extremely simple that differs from standard model, and compare main theoretical predictions regarding...