We present an innovative adaptive, model following control scheme and apply it to control a chaotic system with unknown parameters. We illustrate the proposed approach with control of Duffing oscillator problem. The same idea is used to solve three important problems: suppression of chaos, anticontrol of chaos and chaos synchronization. We propose to use ‘approximators’ linearly parameterized b...

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...

We study the nonlinear oscillations of a forced and weakly dissipative spring– magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet–spring system. The second coil, located below the first, excited with an ac current, provides the osc...

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 ...

An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the generalized harmonic balance method in which analytical approximate solutions have a rational form. This approach gives us not only a truly periodic solution but also the frequency of motion as a function of the amplitude of oscillation. Three truly nonlinear oscillators ...

Title of dissertation: NOISE-INFLUENCED DYNAMICS OF NONLINEAR OSCILLATORS J. Edmon Perkins, Doctor of Philosophy, 2015 Dissertation directed by: Professor Balakumar Balachandran Department of Mechanical Engineering Noise is usually considered detrimental to the performance of a system and the effects of noise are usually mitigated through design and/or control. In this dissertation, noise-influ...

Duffing Oscillator is well known for its chaotic behaviour. This paper aims at clustering of emotions from the EEG response to external audio-visual stimulus used for excitation of a subject. The EEG signal corresponding to a specific emotive stimulus is used as an excitation input to a non-linear Duffing Oscillator dynamics, and the phase trajectory plots of the two state variables of the osci...