The dynamics of a two-degree-of-freedom nonlinear system consisting of a grounded Duffing oscillator coupled to an essentially nonlinear attachment is examined in the present study. The underlying Hamiltonian system is first considered, and its nonlinear normal modes are computed using numerical continuation and gathered in a frequencyenergy plot. Based on these results, the damped system is th...

For solving nonlinear boundary value problems (BVPs), a main difficulty of using Adomian’s method is to find a canonical form which takes into account all the boundary conditions of the problem. This difficulty is overcome by using a modification for Lesnic’s approach developed in this paper. The effectiveness of the proposed procedure is verified by two nonlinear problems: the nonlinear oscill...

This paper develops a design method and theoretical analysis for piecewise nonlinear oscillators that have desired circular limit cycles. Especially, the mathematical proof on existence, uniqueness, stability of cycle is shown oscillator. In addition, relationship between parameters in oscillator rotational directions periods trajectories investigated. Then, some numerical simulations show has ...

The present paper introduces a new, fourth order, analogue chaos generator, aiming at noise, random pulse and spread spectrum signal applications. The proposed system has a simpler implementation compared to other circuits reported in the literature, using only one nonlinear element, namely a Schmitt trigger type hysteretic block, and leading to a uniform circuit structure. The analysis of the ...

We examine various phenomena induced by white Gaussian random perturbations in the response of nonlinear dynamical systems. In the rst part of this work, digital and analog experiments are conducted on a simple single-degree-of-freedom oscillator with piecewise linear restoring force and harmonic forcing. They reveal that small noise perturbations can give rise to large deviations of the respon...

 Abstract—Many natural and manmade dynamical systems that are modeled as large nonlinear multi-oscillator systems like power systems are hard to analyze. For such systems, we propose a nonlinear modal decoupling (NMD) approach inversely constructing as many decoupled nonlinear oscillators as the system’s oscillation modes so that individual decoupled oscillators can be easily analyzed to infer...

In a recent paper [1] Cariñena et al analyzed a non-polynomial onedimensional quantum potential representing an oscillator which they argued was intermediate between the harmonic and isotonic oscillators. In particular they proved that it is Schrödinger soluble, and explicitly obtained the wavefunctions and energies of the bound states. In this paper we show that these results can be obtained m...

The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical...

P. Bhupathi, ∗ Peter Groszkowski, † M.P. DeFeo, Matthew Ware, Frank K. Wilhelm, 3 and B.L.T. Plourde Department of Physics, Syracuse University, Syracuse, New York 13244-1130 Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, 200 University Ave W, Waterloo, ON, N2L 3G1, Canada Theoretical Physics, Saarland University, 66123 Saarbrücken, Germany (Dat...

We investigate the impact of nonlinear damping on the dynamics of a nanomechanical doubly clamped beam. The beam is driven into nonlinear regime and the response is measured by a displacement detector. For data analysis we introduce a nonlinear damping term to Duffing equation. The experiment shows conclusively that accounting for nonlinear damping effects is needed for correct modeling of the ...