In this paper, we present a numerical scheme using uniform Haar wavelet approximation and quasilinearization process for solving some nonlinear oscillator equations. In our proposed work, quasilinearization technique is first applied through Haar wavelets to convert a nonlinear differential equation into a set of linear algebraic equations. Finally, to demonstrate the validity of the proposed m...

In this paper, we discuss the definition of Q factor for nonlinear oscillators. While available definitions of Q are often limited to linear resonators or oscillators with specific topologies, our definition is applicable to any oscillator as a figure of merit for its amplitude stability. It can be formulated rigorously and computed numerically from oscillator equations. With this definition, w...

We study experimentally chaos synchronization of nonlinear optoelectronic oscillators with time-delayed mutual coupling and self-feedback. Coupling three oscillators in a chain, we find that the outer two oscillators always synchronize. In contrast, isochronal synchronization of the mediating middle oscillator is found only when self-feedback is added to the middle oscillator. We show how the s...

The relationship between the topology and collective function of a nonlinear oscillator network was investigated using nonlinear electrochemical oscillators. The constitutive experiments showed that the physiological robustness in the living system is due to their topological redundancy and asymmetry in the nonlinear network. key words: nonlinear oscillator, complex network, physiological funct...

The nonlinear Kuramoto equations for n coupled oscillators are derived and studied. The oscillators are defined to be synchronized when they oscillate at the same frequency and their phases are all equal. A control-theoretic viewpoint reveals that synchronized states of Kuramoto oscillators are locally asymptotically stable if every oscillator is coupled to all others. The problem of synchroniz...

We present an adequate analytical approach to the description of nonlinear vibration with strong energy exchange between weakly coupled oscillators and oscillatory chains. The fundamental notion of the limiting phase trajectory (LPT) corresponding to complete energy exchange is introduced. In certain sense this is an alternative to the nonlinear normal mode (NNM) characterized by complete energ...

Four fractal nonlinear oscillators (The Duffing oscillator, attachment Toda and a oscillator) are successfully established by He’s derivative in space, their variational principles obtained semi-inverse transform method. The approximate frequency of the four found simple formula. results show formula is powerful tool to class oscillators.

In this paper, we propose the first numerical study of nanotube-based torsional oscillators via developing a new multiscale model. The edge-to-edge technique was employed in this multiscale method to couple the molecular model, i.e., nanotubes, and the continuum model, i.e., the metal paddle. Without losing accuracy, the metal paddle was treated as the rigid body in the continuum model. Torsion...

We propose a general strategy for designing coupling functions in order to achieve a desired amplitude dynamics in coupled nonlinear oscillators. The target dynamics achieved by the proposed control schemes is a fixed-point motion at a desired amplitude level or a periodic motion at a desired frequency. The control schemes are illustrated with Rössler and Hindmarsh-Rose oscillators.