The space of Null Lagrangians is the least investigated territory in dynamics since they are identically sent to zero by their Euler-Lagrange operator and thereby having no effects on equations motion. A humble effort discover relevance these made introducing a generalized procedure (with respect recent introduced authors this paper) that takes advantage null-ness construct non-standard represe...

This study investigates the wavelet-based system identification capabilities on determining nonlinearity based impulse response function. Wavelet estimates of instantaneous envelopes and frequency are used to plot backbone curve. wavelet estimate is then values parameter for system. Two weakly nonlinear oscillators, which Duffing Van der Pol have been analyzed using this approach. A case a mode...

Interconnected systems are widespread in modern technological systems. Designing a reliable control strategy requires modeling and analysis of the system, which can be complicated, or even impossible, task some cases. However, current developments data sensing, processing, storage make data-driven techniques an appealing alternative solution. In this work, design methodology decentralized is de...

We study dynamics of a ring three unidirectionally coupled double-well Duffing oscillators for different values the damping coefficient: fixed dumping, proportional to time, and inversely time. The in all cases is analyzed through time series, Fourier Hilbert transforms, Poincar\'e sections, as well bifurcation diagrams Lyapunov exponents with respect coupling strength. In first case, we observ...

To apply effective methods to analyze and distinguish all kinds of response patterns is an important issue of nonlinear dynamics. This paper contributes to develop an alternative Poincaré section method to analyze and identify the whirl responses of a nonlinear oscillator. This integration for analyzing high-order harmonic and chaotic motions is used to integrate the distance between state traj...

A modified variational approach called Global Error Minimization (GEM) method is developed for obtaining an approximate closed-form analytical solution for nonlinear oscillator differential equations. The proposed method converts the nonlinear differential equation to an equivalentminimization problem. A trial solution is selectedwith unknown parameters. Next, the GEM method is used to solve th...

Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). A Duffing oscillator is widely used as an archetypical model of mechanical resonators with nonlinear elastic behavior. In contrast, nonlinear dissipation effects in micromechanical oscillators are often overlooked. In this work, we consider a doubly clamped micromechanical beam oscillator,...

A method for the development of mathematical models for dynamic systems with arbitrary nonlinearides from measured data is described. The method involves the use of neural networks as embedded processors indynamic system simuation models. The technique is demonstrated through generation of models for anharmonic oscillators described by the Duffing Equation and the Van der Pol Equation from meas...