Accurately predicting the onset of large behavioral deviations associated with saddlenode bifurcations is imperative in a broad range of sciences and for a wide variety of purposes, including ecological assessment, signal amplification, and microscale mass sensing. In many such practices, noise and non-stationarity are unavoidable and everpresent influences. As a result, it is critical to simul...

We consider the deterministic escape dynamics of a chain of coupled oscillators under microcanonical conditions from a metastable state over a cubic potential barrier. The underlying dynamics is conservative and noise free. We introduce a two-dimensional chain model and assume that neighboring units are coupled by Morse springs. It is found that, starting from a homogeneous lattice state, due t...

Motivated by recent experimental progress to readout quantum bits implemented in superconducting circuits via the phenomenon of dynamical bifurcation, transitions between steady orbits in a driven anharmonic oscillator, the Duffing oscillator, are analyzed. In the regime of weak dissipation a consistent diffusion equation in the semiclassical limit is derived to capture the intimate relation be...

We present the noise-free escape of a chain of linearly interacting units from a metastable state over a cubic on-site potential barrier. The underlying dynamics is conservative and purely deterministic. The mutual interplay between nonlinearity and harmonic interactions causes an initially uniform lattice state to become unstable, leading to an energy redistribution with strong localization. A...

We examine the Mielnikov criterion for transition to chaos in case of one degree of freedom nonlinear oscillator with non symmetric potential. This system subjected to an external periodic force shows homoclinic transition from regular vibrations to chaos just before escape from the potential well. Especially we study the effect of a second resonant excitation with different phase on the system...

We consider a stochastic environment with two time scales and outline a general theory that compares two methods to reduce the dimension of the original system. The first method involves the computation of the underlying deterministic center manifold followed by a “näıve” replacement of the stochastic term. The second method allows one to more accurately describe the stochastic effects and invo...

The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape...

We investigate analytical methods to predict the long-time cumulative eects of noise perturbations on nonlinear dynamical systems. The study of such perturbations addresses the problem of the global stability of nonlinear systems with multiple coexisting attractors. Indeed small random perturbations can cause large excursions of the system from a nominal steady state, and hence induce transitio...