Nervous networks in the spinal marrow are capable to produce rhythmic movements, such as: swimming, jumping, and walking. These specialised nervous systems are known as central pattern generators (CPGs). Nonlinear oscillators can be used in control systems of locomotion as pattern generators similar to the pattern of human gait, providing the approach trajectories of the legs. The objective of ...

 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...

A rational elliptic balance method is introduced to obtain exact and approximate solutions of nonlinear oscillators by using Jacobi elliptic functions. To illustrate the applicability of the proposed rational elliptic forms in the solution of nonlinear oscillators, we first investigate the exact solution of the non-homogenous, undamped Duffing equation. Then, we introduce first and second order...

Oscillators are used in many integrated RF circuits. Since their behavior is highly nonlinear, full system simulation can be expensive. Furthermore, the behavior of an oscillator can be (un)intendedly perturbed by that of other components and oscillators. We apply a method to build nonlinear phase macromodels of voltage controlled oscillators and show how these can be used to predict the behavi...

We analyze a model for the synchronization of nonlinear oscillators due to reactive coupling and nonlinear frequency pulling motivated by the physics of arrays of nanoscale oscillators. We study the model for the mean field case of all-to-all coupling, deriving results for the onset of synchronization as the coupling or nonlinearity increase, and the fully locked state when all the oscillators ...

Modeling of large amplitude of structures such as slender, flexible cantilever beam and fluid-structure resting on nonlinear elastic foundations or subjected to stretching effects often lead to strongly nonlinear models of Duffing equations which are not amendable to exact analytical methods. In this work, explicit analytical solutions to the large amplitude nonlinear oscillation systems of cub...

For most practical purposes, the focus is often on obtaining statistical moments of the response of stochastically driven oscillators than on the determination of pathwise response histories. In the absence of analytical solutions of most nonlinear and higherdimensional systems, Monte Carlo simulations with the aid of direct numerical integration remain the only viable route to estimate the sta...

In this paper, an aproximate analytical method called the differential transform method (DTM) is used as a tool to give approximate solutions of nonlinear oscillators with fractional nonlinearites. The differential transformation method is described in a nuthsell. DTM can simply be applied to linear or nonlinear problems and reduces the required computational effort. The proposed scheme is base...