We propose two van der Pol oscillators with high-order nonlinearities coupled with an inductor and investigate various types of multimode oscillations. We confirm that these oscillations are stably excited by numerical calculations. In particular, we show the multimode oscillations in the thirteenth and fifteenth-power oscillator systems (the coupled oscillators with thirteenth and fifteenthpow...

We study the periodic solutions of equations with asymmetric nonlinearities ``at resonance'' with the Fuc @ k spectrum. We compute the associated topological degree and prove existence, multiplicity, and stability of large-amplitude oscillations for equations with a small friction term. Such equations can be viewed, e.g., as simple models for investigating vertical oscillations of long-span sus...

We study the response of a large array of coupled nonlinear oscillators to parametric excitation, motivated by the growing interest in the nonlinear dynamics of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). Using a multiscale analysis, we derive an amplitude equation that captures the slow dynamics of the coupled oscillators just above the onset of parametric oscilla...