Journal ArticleDOI
Spectral analysis of a nonlinear oscillator driven by random and periodic forces. I. Linearized theory
TLDR
In this article, the authors combined the techniques of statistical and harmonic linearization to develop a linearized approximation theory for the calculation of the second-order statistics (i.e., autocorrelation functions and spectral densities) of nonlinear systems driven by both random and periodic forces.Abstract:
We have combined the techniques of statistical and harmonic linearization to develop a linearized approximation theory for the calculation of the second-order statistics (i.e., autocorrelation functions and spectral densities) of nonlinear systems driven by both random and periodic forces. For the special case of a Duffing oscillator (a damped anharmonic oscillator with a cubic nonlinearity) driven by Gaussian white noise and by a sinusoidal force, explicit expressions for the renormalized (linearized) frequency, the autocorrelation function, and the spectral density of the oscillator displacement in terms of all the system parameters have been derived. We have determined the region of the parameter space in which the applied periodic force has a significant influence on the second-order statistics of the oscillator.read more
Citations
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Dynamical aspects of animal grouping: Swarms, schools, flocks, and herds
Akira Okubo,Akira Okubo +1 more
TL;DR: An attempt is made to describe the motion of grouping individuals kinematically as distinct from simple diffusion or random walk, to model the grouping on the basis of dynamics of animal motion, and to interpret the grouping from the standpoint of advection-diffusion processes.
Journal ArticleDOI
Harmonic noise: Effect on bistable systems
TL;DR: In this paper, the coordinate of a white noise driven harmonic oscillator is used as a stochastic source term in bistable dynamics, which gives rise to resonance phenomena due to a peak in the spectrum.
Journal ArticleDOI
Bistable oscillator driven by two periodic fields
TL;DR: In this paper, two periodic fields acting on a bistable oscillator are assumed to have different timescales, which allows the exclusion of one of these fields via the separation of timecales.
Journal ArticleDOI
Stochastic resonance in bistable confining potentials
TL;DR: In this paper, the effects of confining conditions on the occurrence of stochastic resonance (SR) in continuous bistable systems were studied by means of double-well potentials that diverged like |x|q for |x |↦∞.
Journal ArticleDOI
Noise effects in an electronic model of a single neuron
TL;DR: This work considers a simple electronic circuit model of a single neuron assumed to be driven by an external signal comprising constant and random components, which gives rise to critical behavior including the onset of hysteresis phenomena even for system parameter values that would not otherwise support such behavior.
References
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Journal ArticleDOI
Equivalent Linearization Techniques
TL;DR: In this paper, the method of equivalent linearization of Kryloff and Bogoliubov is generalized to the case of nonlinear dynamic systems with random excitation, applied to a variety of problems, and the results are compared with exact solutions of the Fokker-Planck equation.
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Brownian motion of a nonlinear oscillator
Mordechai Bixon,Robert Zwanzig +1 more
TL;DR: In this paper, the authors derived linear transport laws for the motion of the average position and velocity of an oscillator undergoing ordinary Brownian motion, and the resulting linear equations are valid for only small deviations of average values from thermal equilibrium.