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Titlebook: IUTAM Symposium on Nonlinear Stochastic Dynamics; Proceedings of the I N. Sri Namachchivaya,Y. K. Lin Conference proceedings 2003 Springer

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Experiments on Large Fluctuationsbasis of the Hamiltonian theory of fluctuations, the non-equilibrium distribution is calculated for the whole phase space, and determined numerically for different values of noise intensity. It is found that there are singularities which are shifted with respect to those seen in the zero-noise limit
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Stochastic Averaging: Some Methods and Applicationsetric properties of the structure will be determinant in the response analysis..In this contribution, we only deal with dimension one. Amplitude-phase variables, which are inspired by action-angle variables for Hamiltonian systems, are introduced. The main interest is that they are computable in an
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The Reduction of Potential Diffusions to Finite State Markov Chains and Stochastic Resonance white noise perturbation of intensity ε. If its trajectories amplify the small periodic perturbation in a ‘best possible way’, it is said to be in stochastic resonance. A lower bound for the ratio of amplitude and logarithm of the period above which quasi-deterministic periodic behavior can be obse
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Stochastic Averaging Near Homoclinic Orbits Via Singular Perturbations consider the Freidlin-Weber problem (a Newtonian particle in a double-well potential). To show the Freidlin-Weber convergence result, we develop a perturbed test function via a boundary-layer PDE near the homoclinic orbit. Solvability of this PDE is equivalent to the glueing conditions of Freidlin-
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Dynamics of Globally Coupled Noisy Excitable Elements: The Fitzhugh-Nagumo Casele element and for the globally coupled system. We introduce an efficient way to numerically solve this Fokker-Planck equation and show that the external driving force leads to a classical resonance when its frequency matches the underlying systems frequency. This resonance is also investigated anal
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Lyapunov Exponents and Stability for the Stochastic Duffing-Van der Pol Oscillator space. If λ > 0 then the process {(.., x.): . > 0} is positive recurrent on R. {(0,0)} with stationary probability measure μ, say. For λ > 0 let . denote the almost sure Lyapunov exponent obtained by linearizing the same equation along a typical stationary trajectory in .. ∖{(0,0)}. The sign of . i
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