The global attraction is established for all finite energy solutions to a model U(1)-invariant nonlinear Klein-Gordon equation in one dimension coupled to a finite number of nonlinear oscillators: We prove that each finite energy solution converges as t → ±∞ to the set of all “nonlinear eigenfunctions” of the form φ(x)e−iωt if all oscillators are strictly nonlinear, and the distances between al...

The current paper focuses on some analytical techniques to solve the non-linear Duffing oscillator with large nonlinearity. Four different methods have been applied for solution of the equation of motion; the variational iteration method, He’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. The results reveal that approxim...

We present a Kolmogorov-like algorithm for the computation of normal form in neighborhood an invariant torus `isochronous' Hamiltonian systems, i.e., systems with Hamiltonians $\mathcal{H}=\mathcal{H}_0+\varepsilon \mathcal{H}_1$ where $\mathcal{H}_0$ is $N$ linear oscillators, and $\mathcal{H}_1$ expandable as polynomial series oscillators' canonical variables. This method can be regarded anal...

We study the clusterization of phase oscillators coupled with delay in complex networks. For the case of diffusive oscillators, we formulate the equations relating the topology of the network and the phases and frequencies of the oscillators (functional response). We solve them exactly in directed networks for the case of perfect synchronization. We also compare the reliability of the solution ...

Enhancement of heat and mass transfer and decrease of energy dissipation are great necessities of the evolution of fluid flow devices. Utilizing oscillatory or pulsatile fluid flow for periodic disturbing of velocity and thermal boundary layers is one of the methods with exciting results. Passive methods of generating oscillatory flow are preferred to active methods because of simplicity, no ne...

Multiphase clocks are very useful for realizing high-speed data processing systems with low-speed circuit elements. Triggered in sequence by equally-spaced N-phase clock signals, multiphase systems can achieve N-times higher operating frequencies than single-phase clocked systems. For this reason, multiphase clocks are often used for such applications as high-speed analog-digital converters (AD...

Currently, the interest in monitoring the vibration of dynamical systems has been increasing. For example, large and complex air and space structures include vibration monitoring systems to forecast sudden failures. Such vibration monitoring is used to diagnose structural health by analyzing vibration characteristics (such as frequency and amplitude). Among the vibration characteristics used, t...

This study aims to test the hypothesis that handwriting is governed by the dynamics of non-linear coupled oscillators. Accordingly, its first goal is to identify preferred, basic graphic shapes corresponding to spontaneously stable combinations of the two frequency-locked oscillatory x-y components of the trajectories. Six participants were required to produce 26 ellipsoids of varying eccentric...

We treat a chain of oscillators with linear stiffness and internal external cubic non-linearities. The method harmonic balance is used to determine the non-linear modes Hamiltonian system. For each equilibrium point, stability analysis performed by means associated monodromy matrix. numerical results shows that branch points, limit points Neimark–Sacker bifurcations exist in aim paper study how...