Related papers: Nonlinear normal modes in electrodynamic systems: …
Many intriguing properties of driven nonlinear resonators, including the appearance of chaos, are very important for understanding the universal features of nonlinear dynamical systems and can have great practical significance. We consider…
Recent advances in the study of synthetic dimensions revealed a possibility to employ the frequency space as an additional degree of freedom which allows for investigating and exploiting higher-dimensional phenomena in a priori…
We prove the existence of nonlinear normal modes for general systems of two coupled nonlinear oscillators. Facilitating the comparison principle for ordinary differential equations it is shown that there exist exact solutions representing a…
We describe linear and nonlinear modes in a ring-shaped waveguide with localized gain and dissipation modeled by two Dirac $\delta$ functions located symmetrically. The strengths of the gain and dissipation are equal, i.e., the system obeys…
Many nonlinear systems are described by eigenmodes with amplitude-dependent frequencies, interacting strongly whenever the frequencies become commensurate at internal resonances. Fast energy exchange via the resonances holds the key to rich…
The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system.…
The concept of nonlinear modes is applied in order to analyze the behavior of a model of woodwind reed instruments. Using a modal expansion of the impedance of the instrument, and by projecting the equation for the acoustic pressure on the…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
Many physical, chemical and biological processes rely on intrinsic oscillations to employ resonance responses to external stimuli of certain frequency. Such resonance phenomena in biological systems are typically explained by one of two…
As a model of coupled nano-electromechanical resonantors we study two nonlinear driven oscillators with an arbitrary coupling strength between them. Analytical expressions are derived for the oscillation amplitudes as a function of the…
For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…
We demonstrate the application of the efficient semi-inverse asymptotic method to resonant interaction of the nonlinear normal modes belonging to different branches of the CNT vibration spectrum. Under condition of the 1:1 resonance of the…
We consider a sub-wavelength periodic layered medium whose slabs are filled by arbitrary linear metamaterials and standard nonlinear Kerr media and we show that the homogenized medium behaves as a Kerr medium whose parameters can assume…
A nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the…
We study the modes and stability of non - isothermal coronal loop models with different intensity values of the equilibrium magnetic field. We use an energy principle obtained via non - equilibrium thermodynamic arguments. The principle is…
The oscillatory response of nonlinear systems exhibits characteristic phenomena such as multistability, discontinuous jumps and hysteresis. These can be utilized in applications leading, e.g., to precise frequency measurement, mixing,…
The energy transfer between different subsystems or different vibration modes is always one of the most interested problems in the study of the resonance phenomena in coupled nonlinear dynamical systems. With an optomechanical system…
The vacuum is expected to exhibit electromagnetic nonlinearity. We demonstrate the properties of nonlinear electromagnetic wave in a two-dimensional rectangular cavity by calculating the nonlinear correction for two classical standing…
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…
Nonlinear energy exchange between vibrational modes underlies phenomena ranging from internal resonance to wave mixing, yet modal interactions are typically inferred from frequency-domain signatures rather than directly observed in space.…